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EC Level 

D C Green 



| ERE 




Radio Systems III 

A textbook covering the Level III syllabus 
of the Technician Education Council 

DC Green 


Senior Lecturer in Telecommunication Engineering 

Willesden College of Technology 


SSiON No. 



CA i c.vj^t\"Y 





39 Parker Street, London WC23 5PB 

Associated Companies 

Copp Clark Ltd, Toronto 
Fearon Publishers Inc, Belmont, California 
Pitman Publishing New Zealand Ltd, Wellington 
Pitman Publishing Pty Ltd, Melbourne 

© D. C. Green 1979 

First published in Great Britain 1979 

All rights reserved. No part of this publication may be reproduced, 
stored in a retrieval system, or transmitted, in any form or by any 
means, electronic, mechanical, photocopying, recording and/or 
otherwise without the prior written permission of the publishers. 
This book may not be lent, resold, hired out or otherwise disposed 
of by way of trade in any form of binding or cover other than that 
in which it is published, without the prior consent of the publishers. 
This book is sold subject to the Standard Conditions of Sale of Net 
Books and may not be resold in the UK below the net price. 

Text set in 10/12 Times Roman. 

Printed by photolithography and bound in Great Britain at The 

Pitman Press, Bath 

ISBN 273 01134 


1 Amplitude Modulation • 1 

Introduction • 1 

Principles of amplitude modulation • 1 

Modulation factor • 5 

Power contained in an amplitude-modulated wave • 6 

R.M.S. value of an amplitude-modulated wave • 8 

Double-sideband suppressed-carrier amplitude 

modulation • 9 
Single-sideband suppressed-carrier amplitude 

modulation • 10 
Single sideband compared with double sideband • 11 
Independent-sideband amplitude modulation • 12 
Vestigial-sideband amplitude modulation • 14 
Measurement of amplitude-modulated waves ■ 15 
Exercises • 18 

2 Frequency Modulation • 20 

Introduction • 20 

Principles of frequency modulation • 20 
Phase modulation • 27 
Signal-to-noise ratio in f.m. systems • 28 
Pre-emphasis and de-emphasis • 30 
Relative merits of amplitude, frequency, and phase mod- 
ulation • 35 
Measurement of a frequency-modulated wave • 36 
Exercises • 37 

3 Modulators and Demodulators • 39 

Introduction • 39 
Amplitude modulators • 39 
Frequency modulators • 47 
Amplitude demodulators • 51 
Frequency demodulators • 56 
Exercises • 64 



/ 4 Transmission Lines - 67 

^ Introduction • 67 

Matched transmission lines • 67 
Mismatched transmission lines • 71 
Standing wave ratio • 76 
Radio station feeders ■ 78 
Exercises • 79 

5 Aerials • 81 
Introduction • 81 
The yagi aerial • 82 
The rhombic aerial • 88 
The log-periodic aerial • 91 
The parabolic reflector aerial • 95 
Exercises • 97 

/ 6/The Propagation of Radio Waves • 100 

^^ Introduction • 100 
The ionosphere • 101 
The ground or surface wave • 104 
Refraction of an electromagnetic wave • 105 
Critical frequency • 108 
Maximum usable frequency • 109 
Skip distance -111 
Multiple-hop transmissions -111 
The space wave • 111 

Propagation via communication satellite -112 
Tropospheric scatter propagation -112 
Fading -113 

Use of the frequency bands -115 
Exercises -116 

7 Radio-frequency Power Amplifiers • 118 

Introduction • 118 

The Class C radio-frequency power amplifier -119 

Effect of loading • 125 

Class B tuned power amplifiers • 125 

Transistor tuned power amplifiers • 129 

Frequency multipliers • 130 

Anode-modulated Class C tuned amplifiers -131 

Collector-modulated Class C tuned amplifiers • 134 

V.H.F. techniques • 136 

Exercises • 137 

8 Radio Transmitters ■ 140 

Introduction • 140 

Amplitude-modulation transmitters • 140 
Output stages • 145 


V.H.F. mobile transmitters ■ 146 
Frequency synthesis, : • 148 
Frequency-modulation transmitters • 150 
High voltage components and precautions • 152 
Exercises -154 

9 Radio Receivers • 157 

Introduction • 157 

The superheterodyne radio receiver • 157 

Selectivity • 165 

Sensitivity • 166 

Noise figure • 167 

The radio-frequency stage • 168 

The mixer stage • 168 

Ganging and tracking • 169 

The intermediate frequency amplifier -174 

The detector stage and automatic gain control • 175 

Automatic frequency control • 177 

The audio-frequency stage • 179 

The double superheterodyne radio receiver • 179 

Communication receivers • 180 

Measurement of performance of amplitude modulation 

receivers • 183 
Exercises • 187 

10 Radio Receiver Circuits • 190 

Introduction -190 

Mixers • 190 

Crystal and ceramic filters • 195 

Automatic gain control • 198 

Automatic frequency control • 202 

Squelch or muting • 203 

Exercises • 204 

11 Wideband Line and Radio Systems • 207 

Introduction • 207 

Land coaxial systems • 208 

Radio relay systems • 209 

Submarine cable systems -213 

High-frequency radio systems • 214 

Communication satellite systems -215 

Noise and interference in communication 

systems -216 
Choice of carrier frequency and bandwidth • 218 
Exercises ■ 220 

Numerical Answers to Exercises * 221 
Learning Objectives (TEC) • 222 

Index -225 


This book provides a comprehensive coverage of the circuits 
and techniques used in modern radiocommunication systems 
and equipments. 

The Technician Education Council (TEC) scheme for the 
education of telecommunication technicians introduces the 
basic principles of radio systems at the second level and a 
further understanding is provided by the third level unit Radio 
Systems III. This book has been written to provide a complete 
coverage of the Radio Systems III unit. 

Chapters 1 and 2 cover the principles of amplitude and 
frequency modulation while Chapter 3 discusses the various 
kinds of modulator and demodulator circuits in common use. 
The next chapters deal with, respectively, radio-frequency 
transmission lines and the four types of aerial commonly 
employed in modern systems, namely the Yagi, the rhombic, 
the log-periodic and the parabolic reflector. The propagation 
of radio waves is the subject of Chapter 6 and then Chapter 7 
is devoted to the tuned radio-frequency power amplifier. 
Chapters 8 and 9 then deal with the principles and practice of 
modern communication transmitters and receivers operating in 
the h.f . and the v.h.f . bands. Many of the circuits used in radio 
receivers, such as amplifiers and oscillators, are discussed in 
the companion volume Electronics III and are not covered in 
this book. Other circuits usually found in radio receivers, such 
as mixers, crystal filters and squelch circuits are dealt with in 
Chapter 10; this chapter also discusses the various ways in 
which a.g.c. and a.f.c. can be applied to a radio receiver. 
Lastly, Chapter 11 introduces the basic principles of wideband 
multi-channel telephony systems operating over both land and 
radio systems. 

This book has been written on the assumption that the 
reader will possess a knowledge of electronics and radio equi- 
valent to that covered by the TEC level II units, Electronics II, 



The following abbreviations for 

other titles in this series are used in 

the text: 

TSII: Transmission Systems II 

RSII: Radio Systems II 

EII: Electronics II 

EIII: Electronics III 

Radio Systems II and Transmission Systems II. The reader 
should also have studied, or be concurrently studying, the level 
III unit Electronics III since knowledge of the operation of the 
bipolar and field-effect transistors and of integrated circuits is 

The book provides a comprehensive text on radiocommuni- 
cation systems that should be eminently suitable for all non- 
advanced students of radio engineering. 

Acknowledgement is due to the Technician Education 
Council for their permission to use the content of the TEC 
unit in the appendix to this book. The Council reserve the 
right to amend the content of its unit at any time. 

Many worked examples are provided in the text to illustrate 
the principles that have been discussed and each chapter 
concludes with a number of short exercises and longer exer- 
cises. Many of the exercises have been taken from past City 
and Guilds examination papers and grateful acknowledgement 
of permission to do so is made to the Institute. Answers to the 
numerical exercises will be found at the end of the book; these 
answers are the sole responsibility of the author and are not 
necessarily endorsed by the Institute. 



Amplitude Modulation 


Amplitude modulation of a sinusoidal carrier wave is widely 
used in line and radio communication systems as a means of 
shifting, or translating, a signal from one frequency band to 
another. Frequency translation of signals is commonly used for 
two reasons. Firstly, the internationally recommended band- 
width for commercial quality speech is 300-3400 Hz and this 
figure is very much smaller than the available bandwidth of a 
telephone cable. This means that a cable pair is capable of 
simultaneously transmitting a number of speech channels pro- 
vided the channels are each positioned in a different part of 
the frequency spectrum of the cable. This process is known as 
frequency-division multiplex (f.d.m.) and is capable of provid- 
ing up to 10 700 channels over a single coaxial cable pair. 
Secondly, frequency translation of an audio frequency signal 
is also used in all kinds of radio systems. Radio signals are 
transmitted and received by means of aerials, but since no kind 
of aerial can operate at such low frequencies it is necessary to 
shift each signal to some higher frequency. It is, of course, 
necessary to carefully choose the frequency bands to which the 
signals are moved in order to ensure that each service within a 
given geographical area operates at a different frequency. In 
practice, the frequency bands which are used for particular 
purposes are allocated in accord with the recommendations of 
the International Telecommunication Union (I.T.U.). 

Principles of Amplitude Modulation 

To obtain the maximum utilization of an available frequency 
spectrum, it is necessary for signals to be frequency translated 
to occupy different parts of that frequency spectrum. In many of 
the systems to be described later in this book, frequency 


translation of a signal is accomplished by the signal amplitude 
modulating a carrier of appropriate frequency. 

The general expression for a sinusoidal carrier wave is 

v= V c sm(a> c t + 8) (1.1) 

where v is the instantaneous carrier voltage, V c is the peak 
value, or amplitude, of the carrier voltage, w c is 2tt times the 
carrier frequency, and is the phase of the carrier voltage at 
time f = 0. Here, 6 will be taken as being equal to zero. 

For the carrier wave to be amplitude modulated, the amp- 
litude of the carrier voltage must be varied in accordance with 
the characteristics of the modulating signal. Suppose the mod- 
ulating signal is sinusoidal and is given by v = V m sin <o m t, 
where V m is its peak value and <a m is 2tt times its frequency. 
The amplitude of the carrier must then vary sinusoidally about 
a mean value of V c volts. The peak value of this variation 
should be V m volts, and the frequency of the variation should 
be (ojlir hertz. The amplitude of the modulated carrier wave 
is therefore V c + V m sin <w m f, and the expression for the instan- 
taneous voltage of an amplitude-modulated wave is 

v = (V C + V m sin a> m t) sin w c f (1.2) 

Multiplying out, 

v = V c sin (o c t + V m sin <a m t sin w c t (1.3) 

Using the trigonometric identity 

2 sin A sinB=cos(A-B)-cos(A+B) 
equation (1.3) may be rewritten as 

V V 

v = V c sin a> c t+^ cos {<o c -a> m )t-^ cos (<o c +w m )t (1.4) 

This equation shows that a sinusoidally modulated carrier 

wave contains components at three different frequencies: 
the original carrier frequency, f c = wjlir 
the lower side frequency, f c —f m = (<*> c — &> m )/27r 
the upper sidefrequency, f c +f m = (a> c +<u m )/27r 

The modulating signal frequency f m is not present. 
The maximum amplitude of the modulated wave occurs 

when sinw m f = l, and is V c + V m ' 

The minimum amplitude occurs when sin<u m f = — 1, and is 

V -V 

v c * m* 

Fig. 1.1 shows the waveform of a sinusoidally modulated 
wave, the outline of which is known as the modulation en- 
velope. In practice, the modulating signal is rarely sinusoidal; 
when this is the case, each component frequency of the mod- 
ulating signal produces corresponding upper and lower sidefre- 
quencies in the modulated wave, and the modulation envelope 


Fig. 1.1 Amplitude modulated wave 


has the same waveform as the modulating signal. The band of 
sidefrequencies below the carrier frequency is known as the 
lower sideband, and the band above the carrier forms the upper 


A 4 MHz carrier wave is amplitude modulated by the band of 
audiofrequencies 300-3400 Hz. Determine (a) the frequencies con- 
tained in the modulated wave and (b) the bandwidth occupied by the 


(a) Using equation (1.4) the components of the modulated wave are 
(i) The carrier frequency f c =4 MHz, 

(ii) The lower sideband frequencies 4 MHz - (300-3400) Hz or 

3 996 600 Hz to 3 999 700 Hz (Am.) 

(iii) The upper sideband frequencies 4 MHz +(300-3400) Hz or 

4 000 300 Hz to 4 003 400 Hz. (Ans.) 3 * 

(b) The necessary bandwidth = highest frequency -lowest frequency 

= 4 003 400-3 996 600 

= 6800 Hz (Ans.) 
Note that the bandwidth occupied by the modulated wave is equal 
to twice the highest frequency contained in the modulating signal. 
This is always the case when the carrier frequency is higher than the 
highest modulating frequency. 


A carrier wave of frequency 1 MHz and amplitude 10 V is amplitude 
modulated by a sinusoidal modulating signal. If the lower sidefre- 
quency is 999 MHz and its voltage is 20 dB below the carrier amp- 
litude, calculate? the amplitude and frequency of the modulating 
signal. | ^ 


Since the carrier and lower sidefrequency voltages are developed 

across the same impedances, the expression 


Loss = 20 log 10 ( VJ V 2 ) decibels 

can be used. 

20 = 20 log! 

/ Carrier voltage \ 
VSidefrequency voltage/ 

Taking antilog 10 of both sides, 

10 = 

/ Carrier voltage ^ 
VSidefrequency voltage/ 

so that 

Sidefrequency voltage = 1 V 

i i 

r t I t f 



f r -f, f„ t+f, 

f. + f-, 

Fig. 1.2 (a) The frequency spec- 
trum of an amplitude-modulated 
wave, (b) The method of represent- 
ing the sidebands of amplitude 

From equation (1.4), the amplitude of a sidefrequency is equal to 
one-half of the voltage of the modulating signal; therefore 

Modulating signal amplitude = 2 V (Ans.) 

The lower sidefrequency is equal to the carrier frequency f c minus the 
modulating frequency f m , i.e. f c — f m so that 

f m = 1000 - 999 = 1 kHz (Ans.) 

There are two ways in which the frequency components of 
an amplitude-modulated wave may be represented by a 

(1) Each component can be shown by an arrow that is drawn 
perpendicularly to the frequency axis as shown by Fig. 1.2a; it 
has been assumed that the carrier wave, at frequency f c , has 
been modulated by a signal containing two components at 
frequencies f t and / 2 . The lengths of the arrows are drawn in 
proportion to the AMPLITUDES of the components they 
each represent. This method of representing an a.m. wave is 
satisfactory when only a few components are involved but it 
rapidly becomes impractical when speech signals are involved. 

(2) The method of representation usually employed, particu- 
larly in connection with multi-channel telephony systems, is 
shown in Fig. 1.2b. The lower and upper sidebands are each 
represented by a truncated triangle, in which the vertical 
ordinates are made proportional to the modulating FRE- 
QUENCY and no account is taken of amplitude. The upper 
sideband is said to be erect because its highest sidefrequency, 
f c +/ 2 , corresponds to the highest frequency f 2 in the modulat- 
ing signal. Conversely, the lower sideband is said to be in- 
verted because its highest frequency component, f c -f u is 
produced by the lowest modulating frequency f t . 


Modulation Factor 

The modulation factor m of an amplitude-modulated wave is 
given by 


Maximum amplitude — Minimum amplitud e 
Maximum amplitude + Minimum amplitude 


When expressed as a percentage, m is known as the percen- 
tage modulation, or the DEPTH OF MODULATION. For 
sinusoidal modulation the maximum amplitude of the modula- 
tion envelope is, from equation (1.2), V c + V m and the 
minimum amplitude is V c - V m , Hence 

m ■■ 

. (Vc + VJ-(Vc-VJ _Vm 

(V C + VJ + (V C -VJ v c 



Draw the waveform of a carrier wave which has been sinusoidaUy 
amplitude modulated to a depth of 25%. If the amplitude of the 
unmodulated carrier wave is 100 V determine (a) the modulating 
signal voltage, (b) the amplitude of the lower side frequency compo- 


The maximum voltage of the modulated wave is V c + V m and 

V„=mV c . Hence the maximum voltage is 

100(1+0.25) = 125 V 
The minimum voltage of the wave is 

V c (l-m) = 75V 
The required amplitude-modulated waveform is shown in Fig. 1.3 

(a) V„ = mV c =0.25X100 = 25 V (Ans.) 

(b) V LSF =mV c /2=25/2= 12.5 V (Ans.) 

§? +i 

Fig. 1.3 Amplitude-modulated wave 
of modulation depth 25% 


Fig. 1.4 Amplitude-modulated wave 
of modulation depth greater 
than 100% 


The maximum value of the modulation factor is limited to 1 
since this gives a minimum value to the envelope of V c (l — 1) 
or zero. If a greater value of modulation factor is used, the 
envelope will no longer be sinusoidal (Fig. 1.4) and the 
waveform will contain a number of extra, unwanted frequency 

Power Contained in an Amplitude-modulated Wave 

The expression for the instantaneous voltage of an amplitude- 
modulated wave, equation (1.2), can be rewritten in terms of 
the modulation factor m: 

' - /a 

\< -,'-«.; 

i s 

v = V c (l+-r^ sin cj m tj sin w c t (1.7) 

= V c (l 4- m sin co m t) sin a>J 

= V c sin coj +5mV c [cos (<o c — &> m )f-cos (co c + w m )r] 


The power developed by an amplitude-modulated wave is 
the sum of the powers developed by the carrier frequency, 
upper sidefrequency and lower sidefrequency components. 
The carrier power is 

/ v c y l v 2 c 

-^ T; or — r watts 
V/2/ R 2R 

and the power developed by each of the two sidefrequencies is 
(mV c \ 2 1 m 2 V 2 

I TT^f 1 ~ or " watts 

12727 R 8R 

so that the TOTAL POWER is 

V 2 C m 2 V 2 m 2 V 2 c 

P = — --I --I - 

' 2R 8R SR 

-£( I+ TM> + f>~ «■« 

-?dfc '~. 



As previously mentioned, the maximum modulation factor 
used in practice is m = 1, and for this condition P t is one and a 
half times the carrier power. For maximum modulation condi- 
tions, therefore, only one-third of the total power is contained 
in the sidefrequencies. Since it is the sidefrequencies that 
carry the intelligence, amplitude modulation is not a very 
efficient system when considered on a power basis. 


The power dissipated by an amplitude-modulated wave is 100 W 
when its depth of modulation is 40%. What modulation depth m is 
necessary to increase the power to 120 W? 


From equation (1.9), 

™=-V4) - '■-£— 

When the depth of modulation is altered to m, the total power 
increases to 120 W. Therefore 

120 = ^2. (1+im 2 ) 

120x1.08 „ . , 

|m 2 = 1.2x1.08-1 

m = V0.592 = 0.769 (Ans.) 


A 1 kW carrier is amplitude modulated by a sinusoidal signal to a 
depth of 50%. Calculate the power at the lower sidefrequency and 
determine what percentage it is of the total power. 


From equation (1.9) 

P, = 1000(1 +|0.5 2 ) = 1000 + 125 

The carrier power is 1000 W so clearly the total sidefrequency 
power is 125 W. The amplitudes of the two sidefrequencies are equal 
and so the sidefrequencies will dissipate equal powers. Therefore 

Lower sidefrequency power = = 62.5 W (Ans.) 

The total power is 1125 W, hence the lower sidefrequency power 
expressed as a percentage of the total power is 


— — xlOO or 5.56% (Ans.) 


R.M.S. Value of an Amplitude-modulated Wave 

If the r.m.s. voltage of an amplitude-modulated wave is V, 
then the power P t dissipated by that wave in a resistance R is 
given by 

P t =^ = P c (l+|m 2 )W 

The power dissipated by the carrier component alone is 

V 2 
c 2R 


P,_ 2V 2 = P c (l+|m 2 ) 
P c V 2 P c 

2V 2 =V 2 (l+^m 2 ) 

V = ^|V(l+!m 2 ) (1.10) 


The r.m.s. value of the current flowing in an aerial is 50 A when the 
current is unmodulated. When the current is sinusoidally modulated, 
the output current rises to 56 A. Determine the depth of modulation 
of the current waveform. 


From equation (1.10) 

56 = 50V(l+|m 2 ) 

jm 2 

m= V 2 [(ir]) 2_1 ] = - 713 (Ans - 

The double-sideband full-carrier (d.s.b.) system of amplitude 
: modulation can be demodulated by a relatively simple circuit 
which responds to the variations of the envelope of the wave. 
Mainly for this reason the d.s.b. system is used for sound 
_ ^broadcasting in the long and medium wavebands. The dis- 
advantage of d.s.b. working, made apparent by Example 1.5, is 
that the greater part of the transmitted power is associated 
with the carrier component and this carries no information. 
Many radio-telephony systems use a more efficient method of 
amplitude modulation. 


Double-sideband Suppressed-carrier Amplitude Modula- 

The majority of the power contained in an amplitude- 
modulated wave is developed by the carrier component. Since 
this component carries no information, it may be suppressed 
'during the modulation process by means of a BALANCED 
MODULATOR. All the transmitted power is then associated 
with the upper and lower sidebands. 

The waveform of a double-sideband suppressed-carrier 
(d.s.b.s.c.) voltage is shown in Fig. 1.5. Fig. 1.5 has been drawn 
on the assumption that a 10 kHz carrier wave is amplitude 
modulated by a 1 kHz sinusoidal wave to produce lower and 
upper sidef requencies of 9 kHz and 1 1 kHz respectively. With 
the carrier component suppressed, the d.s.b.s.c. waveform is 
the resultant of the 9 kHz and 11 kHz waveforms (Figs 1.5 a 
and b) and is shown in Fig. 1.5 c. The envelope of the resultant 
waveform is not sinusoidal and this is an indication that a 

[Time (ms) 

Time (ms) 

Fig. 1.5 The formation of a 
d.s.b.s.c. wave by adding the com- 
ponents at the lower and upper 
sidef requencies 

Time (ms) 


d.s.b.s.c. signal cannot be demodulated with the simple en- 
velope detector which is available for d.s.b. full carrier demod- 

For demodulation to be achieved, it is necessary for the 
carrier component to be re-inserted at the receiver with both 
the correct frequency and phase. The first of these require- 
ments can be satisfied if the receiver circuitry includes an 
oscillator of sufficiently high stability, such as a crystal oscil- 
lator. The second requirement is much more difficult to satisfy 
and led to the rejection of this version of amplitude modula- 
tion in the past. Nowadays, modern developments, particularly 
in the field of integrated circuits, have considerably reduced 
these difficulties, and ji.s.b.s.c. finds an application in two 
particular systems. These are trie "transmission of the colour 
information in the colour television system of the U.K., and 
the transmission of the stereo information in v.h.f. frequency- 
modulated sound broadcast signals. 

Single-sideband Suppressed-carrier Amplitude Modula- 

The information represented by the modulating signal is con- 
tained in both the upper and the lower sidebands, since each 
modulating frequency f x produces corresponding upper and 
lower sidefrequencies / c ±/i. It is therefore unnecessary to 
transmit both sidebands; either sideband can be suppressed at 
the transmitter without any loss of information. 

When the modulating signal is of sinusoidal waveform, the 
transmitted sidefrequency will be a sine wave of constant 
amplitude. Should this signal be applied to an envelope d.s.b. 
detector, a direct voltage output would be obtained and not 
the original modulating signal. This means that, once again, 
demodulation using an envelope detector is not possible. For 
demodulation to be achieved, the carrier component must be 
re-inserted at the correct frequency. Now, however, the phase 
of the re-inserted carrier does not matter and the design of the 
%, receiver is considerably eased. This method of operation is 
known as single-sideband suppressed-carrier (s.s.b.s.c.) amp- 
litude modulation, frequently known simply as s.s.b. 

The basic principle of operation of an s.s.b. system is shown 
in Fig. 1.6. The modulating signal is applied to a balanced 
modulator along with the carrier wave generated by a high- 
stability oscillator. The output of the balanced modulator 
consists of the upper and lower sidebands only. The carrier 
component is not present having been suppressed by the 
- — -J) action of the modulator. The d.s.b.s.c. signal is then applied to 
the band-pass filter whose function is to remove the unwanted 



Fig. 1.6 The production of an 
s.s.b.s.c. signal 





s.s.b.s.c. signal 

Modulating signal 


f c- f m 

f m 




J, c -.v..t, C 

frequency f c 

[5 > - ■' 


Single Sideband compared with Double Sideband 

Single-sideband operation of a radio system has a number of 
advantages over double-sideband working. These advantages 
are as follows: 

(a) The bandwidth required for an s.s.b. transmission is one 
half the bandwidth that must be provided for a d.s.b. 
signal carrying the same information. The reduced band- 
width per channel allows a greater number of channels 
to be provided by the transmission medium. 

(b) The signal-to-noise ratio at the output of an s.s.b system 
is higher than at the output of the equivalent d.s.b. 
system. The improvement in signal-to-noise ratio has a 
minimum value of 9 dB when the depth of modulation is 
100% and becomes larger as the depth of modulation is 
reduced. Exactly 3 dB of this improvement comes 
about because the necessary bandwidth is reduced by 
half, and noise power is proportional to bandwidth. The 
rest of the improvement" afisesas a result of an increase 
in the ratio sideband-power/total-power. 

(c) A d.s.b. transmitter produces a power output at all times 
whereas an s.s.b. transmitter does not. This results in an 
increase in the overall efficiency of the transmitter. 

(d) Selective fading of d.s.b. radio waves may cause consid- 
erable distortion because the carrier component may 
fade below the sideband level. This allows the sidebands 
to beat together and generate a large number of un- 
wanted frequencies. This type of distortion does not 
occur in an s.s.b. system since the signal is demodulated 
against a locally generated carrier of constant amplitude. 

(e) In a multi-channel telephony system, any non-linearity 
generates intermodulation products, many of which 
would lead to inter-channel crosstalk. The most likely 
sources of non-linearity distortion are the output stages 
of amplifiers since these are expected to handle the 
largest amplitude signals. Suppression of the carrier 
component reduces the amplitude of the signals that are 
applied to the output stages and in so doing minimizes 
the effect of non-linearity. 

The main disadvantage of s.s.b. working is the need for the 
carrier to be re-inserted at the receiver before demodulation 


can take place. This requirement increases the complexity, and 
therefore, the cost of the radio receiver. It is for this reason 
that sound broadcast systems dojipt use single-sideband mod- 

The frequency of the re-inserted carrier must be extremely 
accurate if distortion of the demodulated signal is to be 
avoided. For speech circuits an accuracy of perhaps ±20 Hz 
may be adequate but for telegraphy and data signals ±2 Hz 
accuracy is needed. With modern receivers, the re-inserted 
carrier is generated by a FREQUENCY-SYNTHESIS equip- 
ment of high frequency accuracy and stability. The necessary 
re-insert carrier frequency accuracy is easily achieved. In older 
equipments a low-level pilot carrier is transmitted along with 
the wanted sideband. The pilot carrier has an amplitude of 
about- 16 dB relative to the transmitted sideband, and is used 
in the receiver to operate automatic frequency control (a.f.c.) 
circuitry. The a.f.c. circuitry acts to maintain the frequency of 
the re-inserted carrier within the prescribed limits. 

The output power of an s.s.b. transmitter is usually specified 
in terms of the PEAK ENVELOPE POWER (p.e.p.). The 
p.e.p. is the power which would be developed by a carrier 
whose amplitude is equal to the peak amplitude of the pilot 
carrier and the transmitted sideband. When the pilot carrier is 
not transmitted, or is neglected, the term peak sideband power 
(p.s.p.) is often used instead of p.e.p. 


The output voltage of a sinusoidally modulated s.s.b. transmitter is 
applied across a 600 fl resistance. If the amplitude of the transmitted 
sidefrequency is 60 V, calculate (a) the p.s.p., (b) the p.e.p. Assume a 
pilot carrier is transmitted at a level — 16 dB relative to the transmit- 
ted sidefrequency. 


(a) p.s.p. = 60 2 /600 = 6W (Arts.) 

(b) 16dB = 201og 10 (60/V pc ) or V pc =9.5V. 

Therefore, peak voltage of resultant of sidefrequency and pilot carrier 
is 69.5 V and 

p.e.p. = 69.5 2 /600 = 8.05 W (Ans.) 

Independent-sideband Amplitude Modulation 

The number of s.s.b.s.c. channels which can be transmitted 
over a given transmission medium is determined by the 
minimum frequency separation of the channels. This, in turn, 
is set by the attenuation/frequency characteristics of the band- 
pass filters, since a frequency gap between adjacent channels 


Fig. 1.7 The production of an i.s.b. 



f c ± 'ml 


'c + ' m 






'c + 'ml 

'c - 'm2 




'c-' m2 



L_U J__L 

fc-fm fc f e + f m 



fc-fm f c 
s.s.b. (pilot carrier) 

I 1 LJ 

'c " 'm2 

'c + 'm1 f c- f m2 f c f c + f m\ 


i.s.b. (pilot carrier) 

Fig. 1.8 The frequency spectrum 
diagrams of various amplitude- 
modulated signals 

Fig. 1.9 The sidebands of various 
amplitude-modulated signals 

must be provided in which the filter attenuation can build up. 
Channels can be spaced closer together, and hence further 
economy achieved in the utilization of the available frequency 
spectrum, by the use of the independent sideband (i.s.b.) 

The basic principle of an i.s.b. system is shown by Fig. 1.7. 
Two modulating signals at frequencies f ml and f m2 each mod- 
ulate the same carrier frequency f c . The outputs of the two 
balanced modulators are d.s.b.s.c. waveforms at frequencies 
f c ±f m i and / c ±/ m2 respectively. Two band-pass filters are 
used to select the upper sidefrequency f c +f ml in one channel 
and the lower sidefrequency f c —f m2 in the other. The selected 
sidebands are combined in a hybrid coil to produce a double- 
sideband suppressed-carrier signal in which each sideband 
carries different information. 

The differences between d.s.b., s.s.b. and i.s.b. can be illus- 
trated by means of spectrum diagrams. Fig. 1.8 shows the 
spectrum diagrams for each type of modulation, assuming that 
a carrier of frequency f c is modulated by a single frequency f m , 
or in the case of i.s.b. by two sinusoidal waves at frequencies 
/ ml and f m2 . For a complex modulating signal, the number of 
arrows required is very large and an alternative kind of spec- 
trum diagram is used in which the sidebands are represented 
by truncated triangles. Fig. 1.9 uses this method to illustrate 
the differences between the various amplitude modulation 

fc-h fc-h ' c + 'l 'c + '2 'c"'2 U-h 

f c 

. . s.s.b.s.c. 


f c-h f c-h f c *h f c + f A 


f c -h fc-h f c + fy 


f* + h 


fc-h 'c-'l f c 

s.s.b. (pilot carrier) 

fc-h 'c"'l 'c + '3 'c + '4 


i.s.b. (pilot carrier) 


Vestigial-sideband Amplitude Modulation 

Single and independent sideband operations of a radio system 
are possible because the lowest modulating frequency which 
must be transmitted is 300 Hz. A television signal, on the 
other hand, may include components at all frequencies down 
— K to zero hertz and would, in consequence, present insoluble 
jiltering. difficulties if s.s.b. operation were attempted. Con- 
versely, the highest frequency which must be transmitted in a 
u.h.f. television system is 5.5 MHz and so the use of d.s.b. 
amplitude modulation would demand a minimum r.f. band- 
width of 1 1 MHz. As a compromise between the d.s.b. and 
s.s.b. systems of amplitude modulation, a method known as 
j^ vestigial sideband (v.s.b.) is used. 


5.5 MHz 




^-2 MHz f c -1 MHz f c f c + 1MHz £ + 3 MHz f c + 5 MHz : j f c + 7 MHz 

£ + 2 MHz f„+4MHz £+6 MHz 

Fig. 1.10 Colour television signal 

8 MHz bandwidth 

A vestigial sideband signal consists of all of the upper 
sideband plus a part of the lower sideband (see Fig. 1.10). The 
vestige of the lower sideband that is transmitted is not of 
constant maximum amplitude. The first 1.25 MHz of the lower 
sideband is transmitted at full amplitude and thereafter the 
maximum amplitude falls linearly to zero as shown. The r.f. 
bandwidth occupied by the v.s.b. signal is 8 MHz which is 72% 
of the bandwidth which would be required by the equivalent 
d.s.b. signal. It can be seen that the carrier of the associated 
sound signal is positioned 6 MHz above the vision carrier 

For a colour television signal, the chrominance (colour) 
information is superimposed upon the luminance (mono- 
chrome) signal as shown in the figure by making the chromi- 
nance signal amplitude-modulate a 4.433 618 75 MHz sub- 
carrier frequency. Quadrature _double-sideband suppressed- 
carrier amplitude modulation is used. QUADRATURE 
AMPLITUDE MODULATION is a system in which two 


signals modulate two carriers which are at the same frequency 
but are 90° out of phase with one another* The two sets of 
sidebands producedjby such a process do not become mixed up 
during transmission and can be separately demodulated at the 
receiver if two highly stable 90°-out-of-phase oscillators are 
available to provide the carrier re-inserts. 

Measurement of Amplitude-modulated Waves 

With a d.s.b. amplitude-modulated waveform, the parameter 
that is generally measured is the depth of modulation. This can 
be measured by means of a cathode oscilloscope (c.r.o.), a 
modulation meter, or a true r.m.s. responding ammeter or 


-O I 










Fig. 1.11 Measurement of modula- 
tion factor using a c.r.o. 

(a) Use of a C.R.O. 

An amplitude-modulated wave can be displayed on a c.r.o. in 
two different ways. The signal can be applied to the Y-input 
terminals and the timebase set to operate at the frequency of 
the modulating signal, or perhaps two or three times the 
modulating frequency if more than one cycle of the envelope is 
to be displayed. The modulation envelope is then stationary, 
and an amplitude-modulation envelope, such as that shown in 
Fig. 1.1, is displayed. 

An alternative method, that makes the detection of 
waveform distortion easier, is to connect the modulated wave 
to the Y-input terminals and the modulating signal to the 
X-input terminals with the internal timebase switched off (see 
Fig. 1.11a). The resulting display is then trapezoidal, as shown 
at b. It can be shown that the depth of modulation of the 
displayed waveform is given by 

(a - b)/(a + b) per cent 

The accuracy of the methods is limited mainly by the lack of 
discrimination that results from the need to reduce the peak- 
to-peak variation of the modulated wave into the area of the 
c.r.o. screen. The reduction in measurement accuracy is par- 
ticularly noticeable when there is little difference between the 
maximum a and minimum b dimensions in centimetres, i.e. 
when the modulation factor is small. 

(b) Use of a Modulation Meter 

A modulation meter is an instrument which has been designed 
for the direct measurement of modulation depth. Essentially 
the instrument consists of a radio receiver with a direct- 


Fig. 1.12 The relationship between 
the ratio /// c of the r.m.s. currents of 
amplitude-modulated and unmod- 
ulated waves and the modulation 

coupled diode detector. If the measurement procedure 
specified by the manufacturer is followed carefully, accurate 
measurements of modulation depth can be carried out. 

(c) Use of an R.M.S. Responding Ammeter 

The r.m.s. value of an amplitude-modulated current wave is, 

from equation (1.10), given by 

7 = / c V(l+^m 2 ) 

where I c is the r.m.s. value of the unmodulated current 
waveform. The measurement procedure is as follows. The 
r.m.s. value of the current, with no modulation applied, is 
measured first. Then the modulation is applied, and the new 
indication of the true r.m.s. responding ammeter is noted. The 
modulation factor can be calculated using equation (1.10), or 
in practice, read off from a previously-calculated graph of 
modulation factor plotted against the ratio IJI. 


In a measurement of modulation depth using an r.m.s. responding 
ammeter the unmodulated current was 50 A. Use the graph of Fig. 
1.12 to determine the depth of modulation if the r.m.s. current with 
modulation applied is (a) 55 A, (b) 50.5 A. 











1.0 1.05 1.1 1.15 1.20 1.25 








(a) J/4 = 55/50 =1.1 

Therefore, from the graph, 

Depth of modulation m = 65% (Ans.) 

(b) //£ = 50.5/50 = 1.01 


Depth of modulation m = 14% (Ans.) 

This method of measurement is capable of accurate results 
for higher values of modulation depth, but for smaller values, 
below about 30%, the accuracy suffers because of a lack of 

In the case of a single or an independent sideband signal, 
the main feature of interest is the presence or absence of 
non-linearity distortion, since this will lead to the generation 
of intermodulation products with consequent inter-channel 
crosstalk. The usual method of measurement is to apply two 
audio-frequency sinusoidal waves, of equal amplitude but 
about 1 kHz apart in frequency, to the input terminals of the 
channel. The modulated output signal is then, by some means, 
displayed on the screen of a c.r.o. If the channel operates 
linearly, the two frequencies should beat together to produce 
the waveform shown in Fig. 1.13. Any non-linearity present in 
the channel equipment will manifest itself in the form of 
distortion of the envelope of the beat-frequency waveform. 

Alternatively, if an instrument known as a spectrum analyzer 
is available, the component frequencies of the waveform can 
be individually displayed on the analyzer's c.r.t. screen and 
their amplitudes measured. Fig. 1.136 shows the kind of 
display to be expected. The required degree of linearity can 
then be quoted in terms of the maximum permissible amp- 
litude of the intermodulation products. 


1.1. (a) What are the advantages of single sideband operation of a 
radio system over double sideband? (b) Why is the s.s.b. system 
not used for sound broadcasting? (c) Why is a pilot carrier 
transmitted in many s.s.b. and l.s.b. radio systems? (d) Why can 
modern systems avoid the use of a pilot carrier? 

1.2. Derive an expression for the output power of a double 
sideband amplitude modulated transmitter in terms of the 
unmodulated carrier power and the depth of modulation. The 
output power of a radio transmitter is 1 kW when modulated to a 
depth of 100% . If the depth of modulation is reduced to 50% 
what is the power in each sideband? (C & G) 

Fig. 1.13 (a) The signal waveform, (b) the spectrum diagram at 
the output of an i.s.b. channel whose linearity is under test 


1.3. Explain how a c.r.o. can be used to measure (a) the modulation 
factor of a sinusoidally-modulated a.m. signal, (ft) the gain of 
an amplifier. Discuss the likely source of inaccuracy in each 
method. (C & G ) 

1.4. Distinguish between the terms sidefrequency and sideband, and 
explain what is meant by the envelope of an amplitude- 
modulated waveform. Draw the waveform of a carrier wave 
which has been amplitude-modulated to a depth of 20% by a 
sinusoidal signal. 

1.5. (a) A 50 V carrier wave of frequency 4 MHz is amplitude 
modulated by 10 V sinusoidal voltage. Draw the spectrum 
diagram of the modulated wave if the system used is (i) d.s.b., 
(ii) s.s.b.s.c, (iii) i.s.b.s.c. 

(6) Repeat the above for the case when the modulating signal is 
the commercial speech band of frequencies 300-3400 Hz. 

1.6. (a) Why is the use of double sideband amplitude modulation 
restricted to sound broadcasting? , 

(b) A 600 V carrier wave is amplitude modulated to a depth of 
60%. Calculate (a) the modulating signal voltage, (b) the 
voltage of the lower sidefrequency. 

1.7. (a) What do the initials (i) d.s.b., (ii) s.s.b.s.c, and (iii) i.s.b 
stand for? 

(b) List the advantages of s.s.b.s.c. over d.s.b. 

(c) What is the advantage of i.s.b. over s.s.b,? 

(d) Explain, with the aid of a block diagram, the principle of 
operation of the i.s.b. system. 

1.8. Explain the term depth of modulation as applied to an 
amplitude-modulated wave. Spectrum analysis of a signal 
shows that it comprises a carrier and one pair of sidefrequen- 
cies. Each sidefrequency voltage is 10 dB below the carrier. 
Calculate the depth of modulation and the total signal power if 
the power of the unmodulated carrier is 1 mW. (C & G) 

1.9. (a) Describe a method of displaying a voltage waveform by 
means of an oscilloscope. Illustrate your answer by showing 
how the envelope of an amplitude-modulated signal is dis- 

(b) Draw the envelope of a carrier amplitude-modulated by a 

sine wave, given the following: 

Maximum peak-to-peak amplitude 80 mm 
Minimum peak-to-peak amplitude 40 mm 
Modulating frequency 2 kHz, horizontal scale 80 mm = 1 ms 

Calculate the modulation factor of the signal. 

Short Exercises 

1.10. What is meant by each of the following: (i) d.s.b., (ii) s.s.b., (iii) 
d.s.b.s.c, and (iv) i.s.b.? 

1.11. A 1 MHz carrier is amplitude modulated by a 10 kHz sine 
wave. What frequencies are contained in the modulated 
waveforms if the system is (i) d.s.b., (ii) d.s.b.s.c, and (iii) 

1.12. Draw the spectrum diagram for the signal transmitted to line 
for a 5 -channel system in which channel 1 is directly transmit- 
ted and the remaining channels amplitude-modulate carrier 
frequencies of 9 kHz, 14 kHz, 19 kHz, 24 kHz and 29 kHz. 
Assume d.s.b. operation. 

1.13. A modulating signal occupying the frequency band 68-72 kHz 


amplitude modulates a 100 kHz carrier. What bandwidth is 
occupied by the modulated wave? 

1.14. A 64-68 kHz modulating signal modulates a 50 kHz carrier. 
Determine the bandwidth of the modulated wave. 

1.15. If the power in each sidefrequency of a 25 kW carrier wave is 2 
kW when the carrier is sinusoidally modulated, what is the 
depth of modulation? 

1.16. Compare independent sideband operation of a radio system 
with single-sideband operation. 

1.17. When a test tone is applied to one channel in an i.s.b. system, 
the pilot carrier is 18 dB down on the sidefrequency level. If 
the sidefrequency voltage is 25 V determine the voltage of the 
pilot carrier. 

1.18. Why is the s.s.b.s.c. version of amplitude modulation not used 
for (a) sound broadcasting, (b) television broadcasting, (c) 
international radio-telephony (which uses i.s.b.)? 

1.19. A 100 V 5 MHz carrier wave is amplitude-modulated to a 
depth of 60% by a 3 kHz sine wave and the carrier and upper 
sidefrequency components are suppressed. Draw the waveform 
of the transmitted signal. 

1.20. Draw the waveform of d.s.b. amplitude-modulated wave for the 
case of a rectangular modulating signal with a mark/space ratio 
of 2.1. 



Frequency Modulation 


The reasons for the use of modulation in communication 
systems were discussed in the previous chapter. An alternative 
modulation technique, known as frequency modulation, in 
which the modulating signal varies the frequency^, a carrier 
wave, has a number of advantages over amplitude modulation. 
?~~ Frequency modulation is used for sound broadcasting in the 
v.h.f. band, for the sound signal of 625-line television broad- 
casting, for some mobile systems, and For multi-channel tele- 
phony systems operating in the u.h.f. band. The grice which 
must be paid for some of the advantages of frequency modula- 
tion over d.s.b. amplitude modulation is a wider bandwidth 
^*" *"^',^1„' requirement. If the bandwidth of an f.m. system is no wider 
than the bandwidth of the comparable d.s.b. a.m. system 
(narrow-band frequency modulation, n.b.f.m.), the relative 
merits of the two systems are not easy to determine. 

Principles of Frequency Modulation 

When a sinusoidal carrier wave is frequency modulated, its 
— ~ ^instantaneous frequency is caused to vary in accordance with 
-^" the characteristics of the modulating signal. The modulated 
carrier frequency must vary either side of its nominal unmod- 
ulated frequency a number of times per second equal to the 
modulating frequency. The magnitude of the variation — 
known as the frequency deviation — is proportional to the amp- 
litude of the modulating signal voltage. 

The concept of frequency modulation can perhaps best be 
understood by considering a modulating signal of rectangular 
waveform, such as the waveform shown in Fig. 2.1a. Suppose 
the unmodulated carrier frequency is 3 MHz. The periodic 
time of the carrier voltage is 5 jus and so three complete cycles 




+ J 

7 I 

I I 




3 »_ 

1 2 

5 6 

Time (/us) 





Fig. 2.1 A frequency-modulated J 

Time (/us) 


of the unmodulated carrier wave will occur in 1 ju,s. When, 
after 1 jus the voltage of the modulating signal increases to 
+ 1 V, the instantaneous carrier frequency increases to 4 MHz. 
Hence in the time interval 1 /u.s to 2 /las there are four com- 
plete cycles of the carrier voltage. After 2 tts the modulating 
signal voltage returns to OV and the instantaneous carrier 
frequency falls to its original 3 MHz. During the time interval 
3 ju,s to 4ju,s the modulating signal voltage is -IV and the 
carrier frequency is reduced to 2 MHz; this means that two 
cycles of the carrier voltage occur in this period of time. When, 
after 4 fis, the modulating voltage is again V, the instantane- 
ous carrier frequency is restored to 3 MHz. At t = 5 tts the 
modulating voltage is +2V and, since frequency deviation is 
proportional to signal amplitude the carrier frequency is de- 
viated by 2 MHz to a new value of 5 MHz. Similarly, when the 
modulating voltage is ~2 V, the deviated carrier frequency is 
1 MHz. At all times the amplitude of the frequency modulated 
carrier wave is constant at 1 V, and this means that the 
modulating process does not increase the power content of the 
carrier wave. 

When the modulating signal is of sinusoidal waveform, the 
frequency of the modulated carrier wave will vary sinusoidally; 
this is illustrated by Fig. 2.2. 

Frequency Deviation 

The frequency deviation of a frequency-modulated carrier 
wave is proportional to the amplitude of the modulating signal 
voltage. There is no inherent maximum value to the frequency 
deviation that can be obtained in a frequency-modulation 
system; this should be compared with amplitude modulation 
where the maximum amplitude deviation possible corresponds 
to m = l. 


Modulating signal 


Fig. 2.2 A sinusoidally modulated 
f.m. wave 



Carrier wave 


For any given f.m. system, a maximum allowable frequency 
deviation must be specified since the bandwidth occupied by 
an f.m. wave increases with increase in the frequency devia- 
tion. The maximum frequency deviation which is permitted to 
occur in a particular f.m. system is known as the RATED 
SYSTEM DEVIATION. Since the frequency deviationis di- 
rectly proportional to the mo dulating signal voltage, the choice 
of rated system deviation sets the maximum allowable mod- 
ulating signal voltage that can be applied to the frequency 


A frequency-modulated system has a rated system deviation of 
30 kHz. If the sensitivity of the frequency modulator is 4 kHz/V, what 
is the maximum allowable modulating signal voltage? 


30kHz = 4kHz/VxV m 

where V m is the maximum allowable modulating signal voltage. 


30 kHz _„, ,. . 

V = — = 7.5V (Am.) 

4 kHz/V 

Most of the time the amplitude of the modulating signal 
voltage will be less than its maximum allowable value. Then 
the frequency deviation of the carrier will be smaller than the 
rated system deviation. This can be accounted for by introduc- 
ing a factor k where 

Modulating signal voltage 

k = 

Maximum allowable modulating signal voltage 


The frequency deviation of the carrier frequency is then 
given by the product kf d , where f d is the rated system devia- 
tion. The factor k can have any value between 0, when there is 
no modulating signal, and 1, when the modulating signal has 
its maximum permitted value. 



An f .m. system has a rated system deviation of 75 kHz and this is 
produced by a modulating signal voltage of 10 V. Determine (a) the 
sensitivity of the modulator, and (b) the frequency deviation pro- 
duced by a 2 V modulating signal. 


, . ... 75 kHz 

(a) Sensitivity = =7.5 kHz/V (Am.) 

(b) kf d =^x75 kHz= 15 kHz (Arts.) 

k/ d =7.5kHz/Vx2V=15kHz (Am.) 

The FREQUENCY SWING of an f.m. wave is denned by 
the limits between which the carrier frequency is deviated, i.e. 
twice the frequency deviation. 

Modulation Index 

The modulation index nif of a frequency-modulated wave is 
the ratio of the frequency deviation of the carrier to the 
modulating signal frequency, i.e. 

mf = kfjf m (2.2) 

The modulation index is equal to the peak PHASE DEVIA- 
TION, in radians, of the carrier, and it determines the amp- 
litudes and the frequencies of the components of the mod- 
ulated wave. 

Deviation Ratio 

The deviation ratio D of a frequency-modulated wave is the 
particular case of the modulation index when both the fre- 
quency deviation and the modulating frequency are at their 
maximum values: 

D=fjf mimax) (2.3) 

The deviation ratio is the parameter used in the design of a 
system and its value is fixed. Conversely, the modulation index 
will continually vary as the amplitude and/or frequency of the 
modulating signal changes. 


A 100 MHz carrier wave is frequency modulated by a 10 V 10 kHz 
sinusoidal voltage using a linear modulator. The instantaneous carrier 
frequency varies between 99.95 and 100.05 MHz. Calculate (a) the 


sensitivity of the modulator, (b) the modulation index, (c) the peak 
phase deviation of the carrier. 

Solution • 

(a) The peak frequency deviation is 0.05 MHz. Therefore 

0.05 xlO 6 c rt1tr „, . . . 
Modulator sensitivity = — = 5.0 kHz/V (Ans.) 

(b) From equation (2.2), 

50xl ° 3 c ,a \ 

^ = To^^= 5 (Ans - } 

(c) The peak phase deviation of the carrier is equal to the modulation 
index i.e. 

5 radians (Ans.) 


What will be the new values of the peak frequency and phase 
deviations in the system of Example 2.3 if the amplitude and fre- 
quency of the modulating signal are changed to 20 V and 5 kHz 



If the amplitude of the modulating signal voltage is doubled, the 

frequency deviation of the carrier will also be doubled. Therefore, 

fc/a = 0. 1 MHz =100 kHz (Ans.) 

The peak phase deviation is given by kfjf m . Therefore, 

5x20/10 n J . , A . 

Peak phase deviation = — —— — = 20 radians (Ans.) 

Frequency Spectrum of a Frequency-modulated Wave 

When a sinsusoidal carrier wave of frequency f c is frequency 
modulated by a sinusoidal signal of frequency f m , the mod- 
ulated wave may contain components at a number of different 
frequencies. These frequencies are the carrier frequency and a 
number of sidefrequencies positioned either side of the car- 
rier. The sidefrequencies are spaced apart at frequency inter- 
vals equal to the modulating frequency. The first-order side- 
frequencies are f c ±f m , the second-order sidefrequencies are 
f c ±2f m , the third-order sidefrequencies are / c ±3/ m , and so 

The amplitudes of the various components, including the 
carrier, depend upon the value of the modulation index or 
deviation ratio, as shown by the curves given in Fig. 2.3. Only 
the first nine orders of sidefrequencies have been shown in 
order to clarify the drawing but many more are equally possi- 
ble. The carrier component is zero for values of modulation 
index of 2.405, 5.520 and 8.654. This is in contrast with d.s.b. 
amplitude modulation where the carrier is always present. 








i or 


rd ore 


4th order 



7th order 

8th order g tn or( jer 















Modulation index (or deviation ratio) 

Fig. 2.3 Showing how the amplitudes of the various compo- 
nents of an f.m. wave vary with the modulation index 

Fig. 2.3 can be used to determine the frequencies contained 
within a particular frequency-modulated wave. The amplitudes 
of each component present in the wave are obtained by 
projecting from the modulation index (or deviation ratio) 
value on the horizontal axis, onto^he'appTSpT^Se^urve, and 
thence to the vertical axis. Negative signs are omitted since 
only the magnitude of each component is wanted. 


Plot the frequency spectrum diagrams of a frequency-modulated wave 
having a deviation ratio of (a) 1 and ib) 5. 


The required spectrum diagrams are shown in Figs. 2.4a and b 


The spectrum diagrams of Fig. 2.4 show clearly that an increase in 
the modulation index of an f.m. wave will result in an increase in the 
number of sidefrequencies generated. 


f c-2f m 

fr-3f m f r - 

4 + 24, 


4-84,4-64,4-44,4-24, 4 4 + 24,4 + 44,4 + 64,4 + 84, 
4 - 74, 4 - 54,4 - 34, 4 - 4, 4 '+ 4, 4 + 3^4 + 54, £ + 74, 


Fig. 2.4 Spectrum diagrams of f.m. waves with (a) m f =1, 
<b)m f = 5 


The bandwidth that is necessary for the transmission of an f.m. 
wave is wider than the frequency swing and is given by 
equation (2.4): 

Bandwidth = 2(fc/ d + f m ) (2.4) 

where, as before, kf d is the frequency deviation of the carrier 
and f m is the modulating signal frequency. Equation (2.4) 
assumes that any sidefrequency whose amplitude is less than 
10% of the amplitude of the unmodulated carrier wave need 
not be transmitted. 

An f.m. system will, of course, be designed to transmit the 
most demanding modulating signal. without excessive distor- 
tion. Such a signal is the one whose magnitude produces the 
rated system deviation and whose frequency is the maximum 
to be transmitted by the system. The bandwidth required for 
the satisfactory transmission of this signal is given by equation 

System bandwidth = 2(/ d +/, 

wi (max) 


The accuracy of equations (2.4) and (2.5) can readily be 
checked with the aid of Fig. 2.4. Consider, as an example, the 
B.B.C. v.h.f. frequency-modulated sound_bxoad£^st_system; 
the parameters of this system include a rated system deviation 
of 75 kHz and a maximum modulating frequency of 15 kHz. 
The deviation ratio D is 5 and, from Fig. 2.4ft, the highest 
order sidefrequency that needs to be transmitted (amplitude 
less than ±0.1 on the vertical scale of Fig. 2.3) is the sixth. 


This means that the necessary bandwidth is 
U ±6/ m = 12/ m = 12 x 15 kHz = 180 kHz. 

Using equation (2.5) the required bandwidth is 

2(75 + 15) kHz =180 kHz 

As a second example consider a narrow band system in 
which f d = / m(max) = 3 kHz. For this system the deviation ratio 
is unity and from Fig. 2.3a the highest-order significant side- 
frequencies are the second. The necessary bandwidth is 

. f c ±2f m = 4x3 kHz= 12 kHz 

From equation (2.5) the necessary bandwidth is 
2(3 + 3) kHz = 12 kHz as before 

Power Contained in a Frequency-modulated Wave 

Since the amplitude of a frequency-modulated wave does not 
s=~? vary, the total power contained in the wave is constant and 

•" equal to the unmodulated carrier power. 

Phase Modulation 

When a carrier wave is phase modulated, its instantaneous 
__"~~) phase is made to vary in accordance with the characteristics of 
the modulating signal. The magnitude of the phase deviation is 
proportional to the modulating signal voltage, while the 
number of times per second the phase is deviated is equal to 
the modulating frequency. 

The maximum phase deviation permitted in a phase mod- 
ulation system is known as the RATED SYSTEM DEVIA- 
TION <J> d and, as with frequency modulation, it sets an upper 
limit to the modulating signal voltage. A modulating voltage of 
lesser amplitude will produce a phase deviation equal to fc<£> d , 
where fc has the same meaning as before. The product fc<J> d is 
the modulation index of the phase-modulated wave. Modulat- 
ing the phase of the carrier will at the same time vary the 
instantaneous carrier frequency. The frequency deviation pro- 
duced is proportional to both the amplitude and the frequency 
of the modulating signal. 

Frequency and phase modulation are sometimes grouped 
' :y together and called ANGU^MOJJULATION since they each 
deviate both the frequency and the phaseof the carrier vol- 
tage. The differences between the two types of modulation are 
tabulated in Table 2.1. 


Table 2.1 

Modulation Frequency deviation 

Phase deviation 

Frequency Proportional to voltage 
of modulating signal 

Phase Proportional to both 

voltage and frequency 
of modulating signal 

Proportional to voltage 
and inversely propor- 
tional to frequency of 
modulating signal 

Proportional to voltage 
of modulating signal 

Noise output of 
a.m. receiver 


Fig. 2.5 Triangular noise spectrum 
of an f.m. system 


A carrier wave is angle modulated by a sinusoidal voltage and then 
has a phase deviation of 3 radians and a frequency deviation of 
6 kHz. If the voltage of the modulating signal is doubled and the 
modulating frequency is reduced by half, the frequency deviation is 
unaltered. Is this frequency- or phase-modulation? What is the new 
phase deviation? 


Refering to Table 2.1 it is clear that the carrier has been phase 

modulated. (Ans.) 

New phase deviation = 3x2 = 6 rad (Ans.) 

The frequency spectrum of a phase-modulated wave is ex- 
actly the same as that of the frequency-modulated wave having 
the same numerical value of modulation index. 

Signal-to-Noise Ratio in F.M. Systems 

During its transmission, a frequency modulated signal will be 
subjected to noise and interference voltages. The effect of 
these unwanted voltages is J» vary both the amplitude and the 
phase of the f.m. signal. The amplitude variations thus pro- 
duced have no effect on the performance of the system since 
they will have been removed by a limiter circuit in the radio 
receiver. The phase deviation of the signal, however, means 
that the carrier is effectively frequency modulated by the 
noise, and a noise voltage will appear at the output of the 
radio receiver. 

The magnitude of the output noise voltage is directly prop- 
'ortional to frequency and gives rise to the TRIANGULAR 
NOISE SPECTRUM (Fig. 2.5). The output noise voltage rises 
linearly from zero frequency until, theoretically, at a frequency 
equal to the rated system deviation f d , it is equal to the noise 
output voltage from an a.m. system subject to the same 
noise/interfering voltage. For many systems not all of this 
noise is able to pass through the audio stage of the receiver, 
since the frequency deviation is larger than the audio pass- 


Frequency (kHz) 

Fig. 2.6 Illustrating the effect on 
the noise output of an f.m. system 
of reducing the deviation ratio 

As an example, consider the v.h.f. sound broadcast system 
of the B.B.C.; this system employs a rated system deviation of 
75 kHz and a maximum modulating frequency of 15 kHz, i.e. 
the deviation ratio D is 5. Then, refering to Fig. 2.6, the areas, 
enclosed by the points ABC and ABDE represent, respec- 
tively, the output noise voltages of the f.m. and the a.m. 
systems. Clearly, the nois e out put of the Lm. receiver is 
^ i" smaller than that of t he a.m . receiver. This means that fre- 
quency modulation can provide an increase in the output 

(7 • £-iu s ig n a'-to-noise ratio of a system. This is one of the advantages 
., ^^>m ^ frequency modulation over d.s.b. amplitude modulation. 

^ — The size of the signal-to-noise ratio improvement depends 

upon the rated system deviation used and hence upon the 
system bandw idth a vailabl e. If the frequency deviation of the 
B.B.C. broadcast system were reduced to 15 kHz without 

— - ise changing tne maximum modulating frequency, so that D = \, 
the output noise-voltage would be represented by the area 
enclosed by the points A,B,D in Fig. 2.6. Area ABD is larger 
than area ABC, an indication that the reduction in frequency 
deviation has resulted in an increase in the output noise 
voltage. The signal-to-noise ratiot improvement of an f.m. 
system over an a.m. system is given by equation (2.6): 

Signal-to-noise ratio increase = 20 log 10 DJ3 dB 
where D is the deviation ratio. 



A frequency-modulation system has an output signal-to-noise ratio of 
30 dB when the deviation ratio is 3.5. What will be the output signal- 
to-noise ratio if the deviation ratio is increased to 5? 


New output signal-to-noise ratio = 30 + 20 log 10 (5/3.5) 

= 33.1dB (Ans.) 

The signal-to-noise ratio at the output of a frequency- 
modulation system is a function of the rated system deviation 
chosen. An increase in the deviation will increase the output 
signal-to-noise-ratio but, at the same time (see equation (2.5)), 
also increase the required system bandwidth. Thus, the choice 
of rated system deviation for a particular system must be a 
compromise between the conflicting requirements of maximum 
output signal-to-noise ratio and minimum bandwidth. 

For its v.h.f. sound broadcasts, the B.B.C. use, as previously 
mentioned, a rated system deviation of 75 kHz which gives a 

t Signal-to-noise ratio = (Wanted signal power)/(Unwanted noise 
power) [see EIII] 


deviation ratio of 5 and a minimum bandwidth requirement of 
180 kHz. The sound section of u.h.f. television transmissions 
use a rated system deviation of 50 kHz. This gives a deviation 
ratio of 3.33 and a necessary bandwidth of 130 kHz. The rated 
system deviation chosen for mobile systems is always consider- 
ably smaller than the B.B.C. figures. This is because the need 
for minimum channel bandwidth is of paramount importance, 
while a wide audio-frequency response is not necessary. 
Some typical figures are given in Table 2.2. 

Table 2.2 

Rated system 





frequency (kHz) 












Multi-channel telephony systems are often routed over 
frequency-modulated radio-relay systems operating in the 
s.h.f. band. The frequency deviation of such systems is usually 
quoted as a number of megahertz peak-to-peak deviation. The 
systems are generally set up to give the frequency deviations 
listed in Table 2.3. 

Table 2.3 

System Frequency deviation Note 

600 channel 

200 kHz 

Test tone on 
one channel 

1800 channel 

140 kHz 


Carrying t.v. signal 

8 MHz 

1 V p-p Input 

Pre-emphasis and De-emphasis 

Most waveforms transmitted by communication systems con- 
tain a large number of components at different frequencies. 
Usually the higher-frequency components are of smaller amp- 
litude than the components at lower frequencies. For example, 
the frequencies contained in a speech waveform mainly occupy 
the band 100-10 000 Hz but most of the power is contained at 
frequencies in the region of 500 Hz for men and 800 Hz for 
women. Since the noise appearing at the output of a 
frequency-modulated system increases linearly with increase in 
frequency, the signal-to-noise ratio falls at high frequencies. 


Fig. 2.7 Signal-to-noise ratio at the 
output of an f.m. system 

ig. 2.8 The effect of pre-emphasis 
n the output signal-to-noise ratio of 
n f.m. system 

-Component of signal waveform 

Noise voltage 


This is shown by Fig. 2.7 in which a signal containing compo- 
nents at five different frequencies has been assumed. For a 
multi-channel system this means that the signal-tOHnoise_ ratio 
will be worse injhe highest-frequency channeL To improve the 
signal-to-noise ratio at the higher frequencies, pre-emphasis 
of the modulating signal is applied at the transmitter. 

Refer to Fig. 2.8. The modulating signal is passed through a 
PRE-EMPHASIS network which accentuates the amplitudes 
of the high-frequency components of the signal relative to the 
low-frequency components, before it is applied to the radio 
transmitter. During its transmission from transmitter to re- 
ceiver, noise and interference will be superimposed upon the 
signal so that the output of the radio receiver will exhibit the 
triangular noise spectrum. Now, however, the signal-to-noise 
ratio at the higher frequencies is greater than it would have 
been without pre-emphasis. 







Higher frequency components 




v * 


icked up 





Components of signal 
restored to their 
original amplitude 






To avoid signal distortion it is necessary to restore the 
frequency components of the received signal to their original 
relative amplitude relationships. For this the signal is passed 
through a de-emphasis circuit. The DE-EMPHASIS circuit is 
a network which has an attenuation which increases with 
increase in frequency. The de-emphasis circuit also attenuates 
the high-frequency components of the noise voltage and does 
not, therefore, lose the signal-to-noise ratio improvement 

To ensure that the component frequencies of the received 
signals are restored to their original amplitude relationships, it 
is necessary for the pre- and de-emphasis networks to have 
equal time constants. For example, in the v.h.f. sound broad- 
cast system of the U.K. a time constant of 50 /its is employed. 



12 728 
Frequency (Hz) 


Fig. 2.9 (a) A pre-emphasis circuit, (fa) a de-emphasis circuit, (c) 
pre- and de-emphasis characteristics for 50 /us sound broadcast 

A variety of different networks can be used to provide pre- 
and de-emphasis circuits and Fig. 2.9 shows an example of 
each. The PRE-EMPHASIS CIRCUIT consists of an inductor 
L connected in series with a resistor R L to form the collector 
load of a transistor. The impedance of the collector load will 
increase with increase in frequency and so, therefore, will the 
voltage gain of the amplifier. The time constant of the circuit is 
L/R L seconds (C c is merely a d.c. blocking component). At the 
lower frequencies the impedance of the collector load is R L 
ohms. The impedance Z = \/[i?£ + ((oL) 2 ] will be 3dB larger 
than R L ohms, i.e. R L \l2il, at the frequency at which R L = 
o)L. The 3 dB frequency /j^b is 

fsdB — Rl/2ttL — 

2 ir x (time constant) 



Fig. 2.10 (a) Pre-emphasis charac- 
teristics for multi-channel radio- 
relay systems 


/3dB — 



= 3182 Hz 

At frequencies higher than / 3dB the impedance of the collec- 
tor load and hence the output voltage will double for each 
twofold increase in frequency, i.e. increase at a rate of 
6 dB/octave. This means that the impedance is 9 dB greater at 
6364 Hz and 15 dB greater at 12 728 Hz (see Fig. 2.9c). The 
output-voltage/frequency characteristic of the de-emphasis cir- 
cuit must be the inverse of this and is also shown in the figure. 

The improvement in output signal-to-noise ratio produced 
by the use of pre-emphasis is not easy to assess but for sound 
broadcasting is generally supposed to- b e abo ut 6 dB^ 

A mobile communication radio system will have an audio 
passband of about 300-3000 Hz and a typical pre-emphasis 
characteristic is 6 dB per octave over this band. 

The choice of pre-emphasis characteristic to be used for a 
multi-channel radio-relay system has been made by the 
C.C.I.R. and is given in Fig. 2.10a. Signals carried by the 
low-frequency channels are reduced in amplitude, while sig- 
nals applied to high-frequency channels have their amplitude 
increased; in the case of the top channel by 4 dB. The standard 
frequency deviation is produced at a baseband frequency of 
60.8% of the maximum. 

relative to 200 kHz (db) 


i + 3 

1 +2 



£ +1 








0.1 0.2 1 2 10 

; Normalized frequency (frequency/highest frequency in baseband) 


Many wideband s.h.f. radio systems carry television signals 
instead of multi-channel telephony. The television signal is 
also pre-emphasized but the purpose of the operation is now 
to make it possible for the same modulator to be used for 
both telephony and television. The television signal waveform 
is of non-symmetrical shape, since most of its energy is con- 
tained at low frequencies and the pre-emphasis network re- 
duces the amplitudes of the low-frequency components. The 
t.v. pre-emphasis characteristic is shown in Fig. 2.10b; stan- 
dard frequency deviation is produced at 1.6 MHz. 

Relative Merits of Amplitude, Frequency and Phase Mod- 

The advantages of frequency modulation over d.s.b. amplitude 
modulation are listed below: 

(a) The dynamic _range (the range of modulating signal 
amplitudes from lowest to highest) provided is much 

ative frequency deviation (dB) 

+ + -■ 






)1 0.02 0.05 



5 1 

2 5 U 

Frequency (MHz) 

Fig. 2.10 (fa) Pre-emphasis characteristics for u.h.f. television 



(b) The frequency-modulation transmitter is more efficient. 
There are two reasons for this f firstly, Class C Amplifiers 
can be used throughout the r.f. section of the transmit- 
ter, and secondly, since the amplitude of an f.m. wave is 
constant each r.f. stage in the transmitter can be oper- 
ated in its optimum manner. This is not the case in a 
d.s.b. a.m. transmitter because each of the stages must be 
capable of handling a peak power which can be consid- 
erably larger than the average power. 

(c) Since an f.m. receiver does not respond to any amp- 
litude variations of the input signal, selective fading is 
not a problem. 

(d) The use of frequency modulation provides an i ncrease 
in the output signal-to-noise xatio_oJLthe radio receiver 
provided a deviation ratio greater than unity is used. 
Narrowband f .m. systems do not share this advantage. 

(c) An f.m. receiver has the ability to suppress the weaker 
of two signals which are simultaneously present at its 
aerial terminals at or near the same frequency. The 
CAPTURE RATIO is expressed in dB; the lower the 
value the better. For example, a capture ratio of 4.5 dB 
means that, if the receiver is tuned to a particular signal, 
it will not respond to any other signal whose amplitude 
is 4.5 dB or more below the amplitude of the wanted 

(/) When a multi-channel telephony system is transmitted 
over a radio-relay link, li nearity in the o utput/input 
transfer characteristic of the equipment is of the utmost 
importance in order to minimize inter-channel crosstalk. 
The required linearity is easier to obtain using frequency 

Although phase modulation is very similar to frequency 
modulation, it is rarely used for analogue systems. There are 
two reasons for this; 

(a) Frequency modulation is more efficient than phase mod- 
ulation in its use of the available frequency spectrum. 

(b) Demodulation of a phase-modulated wave is more 
difficult than f.m. demodulation since it requires a very 
stable reference oscillator in the receiver] 

The main disadvantage of frequency modulation is, of 
course, the much wider bandwidjh_jeqmred if the possible 
signal-to-noise ratio improvement is to be realized. For 
narrow-band mobile applications the capture effect may also 
prove to be disadvantageous since when a mobile receiver is 
near the edge of the service area it may be captured by an 
unwanted signal or a noise voltage. 


Measurement of a Frequency-modulated Wave 

The parameter of a frequency-modulated wave that is usually 
measured is the frequency deviation. Commercial f.m. devia- 
tion meters are available but the measurement can be carried 
out by the CARRIER DISAPPEARANCE method. The 
amplitude of the carrier frequency component of an f.m. wave 
is a function of the modulation index. The carrier voltage is 
zero for values of modulation index of 2.405, 5.52, 8.65, etc. 
If, for any one of these modulation indexes, the modulation 
frequency is known, the frequency deviation can be calculated. 

To measure the frequency deviation of an f.m. wave the 
signal is applied to an instrument known as a spectrum 
analyzer. The spectrum analyzer is an instrument which dis- 
plays voltage to a base of frequency (as opposed to a c.r.o. 
which displays voltage to a base of time). The spectrum 
analyzer therefore displays the spectrum diagram of the f.m. 
signal (see Fig. 2.4 for example). It is adjusted to display only 
the carrier and the first-order sidefrequencies. 

With the modulating frequency kept at a constant value, the 
amplitude of the modulating signal is increased from zero, 
which varies the frequency deviation until the carrier first goes 
to zero. Then rty = 2.405 and the frequency deviation can be 
calculated. Further increase in the modulating signal voltage 
will cause the carrier component to reappear and then again 
go to zero when the modulation index becomes 5.52. 


In a measurement of the frequency deviation of an f.m. signal, 
the frequency of a signal generator was set to 3 kHz. Calculate 
the frequency deviation at (a) the first and (b) the second 
carrier disappearance. 


(a) ^ = 2.405=^ 

kf d =2.405 x 3 x 10 3 = 7.215 kHz (Arts.) 

(b) fcf d = 5.52x3xl0 3 = 16.56 kHz (Arts.) 


2.1. (a) What is meant by the following terms in connection with 
frequency modulation: (i) modulation index, (ii) frequency de- 
viation, (iii) practical bandwidth? (b) When the modulation 
index of a certain f.m. transmitter is 7 in a practical bandwidth 
of 160 kHz, what is its frequency deviation? 

2.2. (a) What is the meaning of the term modulation index when 
applied to an f.m. signal? (b) What is the meaning of the term 


modulation factor when applied to an a.m. signal? (c) Describe 
a method of measuring each. (C & G) 

2.3. (a) What do you understand by the following terms: (i) fre- 
quency deviation, (ii) modulation index, (iii) deviation 
ratio? (b) The r.f. bandwidth required for an f.m. transmitter 
is 100 kHz when the modulation index is four. If the modula- 
tion signal level is increased by 6dB, what is (i) the new 
modulation index, (ii) the bandwidth required? (C & G) 

2.4. (a) Briefly explain the purpose of pre-emphasis and de- 
emphasis in f.m. systems, (b) What is the approximate improve- 
ment in output signal-to-noise ratio when pre-emphasis and 
de-emphasis circuits are used? (c) Draw the circuit diagram of 
(i) a pre-emphasis and (ii) a de-emphasis circuit, (d) Indicate 
the components in these circuits upon which the degree of 
emphasis depends. (C & G) 

2.5. (a) Why is the use of frequency modulation confined to the 
v.h.f. band and above as a general rule? (b) Briefly describe 
what you understand by the term capture effect, (c) (i) Indicate 
typical values of frequency deviation and highest modulating 
frequency used in f.m. broadcasting services operating in the 
v.h.f. band; (ii) Using these values calculate the maximum 
percentage band occupancy when the minimum carrier spacing 
is 2.2 MHz for transmitters serving the same area. (C & G) 

2.6. When a certain sinusoid is used to frequency modulate a v.h.f. 
carrier, the required bandwidth is 200 kHz. It is desired to 
retain the same modulation index while reducing the necessary 
bandwidth to 100 kHz. What changes should be made to the 
input to the modulator to achieve the required deviation? 


2.7. Describe, using sketches where necessary, how the amplitude 
and frequency of a modulating signal are conveyed by (a) 
amplitude modulation, (b) frequency modulation. Discuss 
briefly the advantages and disadvantages of f.m. compared with 
a.m. in a v.h.f. communication system. The r.f. bandwidth of an 
f.m. transmitter is 80 kHz when a 6 kHz modulating signal 
is applied. What bandwidth is required if the modulating signal 
level is reduced by 6 dB? 

2.8. Explain why f.m. transmission can give an improved signal-to- 
noise ratio compared with a.m. transmission of the same carrier 
power. What characteristics of f.m. transmission determine the 
magnitude of this improvement? An f.m. radio link having a 
deviation ratio of 10 is to transmit speech occupying the audio 
band up to 3 kHz. What r.f. bandwidth would normally be used 
for this transmission? What would be the effect on (a) the r.f. 
bandwidth and (b) the signal-to-noise ratio if the deviation ratio 
were reduced to 5? (C & G) 

2.9. What is the meaning of the term dynamic range when used in 
conjunction with a modulation system? Explain why it is possi- 
ble for an f.m. system to have a greater range than an a.m. system. 

2.10. Use the graph given in Fig. 2.3 to draw the spectrum diagram 
of a 80 MHz carrier wave frequency modulated with an index 
of 4. What bandwidth is required? 


Short Exercises 

2.11. Draw the circuit diagram of (a) a pre-emphasis circuit and (b) a 
de-emphasis circuit. 

2.12. Why will the full advantages of frequency modulation not be 
realised unless the signal at the output of the i.f. amplifier is 

2.13. Why must frequency modulation be used in conjunction with a 
very high frequency carrier? 

2.14. With which of the following modulation techniques is the 
triangular spectrum of noise associated: (i) a.m., (ii) f.m., (iii) 
both a.m. and f.m. (b) At which of the following does the 
triangular spectrum of noise appear: (i) r.f., (ii) i.f., (iii) a.f.? 

2.15. The r.f. bandwidth required by an f.m. transmitter is 120 kHz 
when the modulation index is 3. What bandwidth is needed if 
the modulation index is increased six times? 

2.16. Briefly explain the differences between frequency modulation 
and phase modulation. 

2.17. Define the following terms used with frequency modulation: (i) 
frequency deviation, (ii) rated system deviation, (iii) modulation 
index, and (iv) deviation ratio. 

2.18. What characteristic of a frequency-modulated wave determines 
(i) the amplitude and (ii) the frequency of the audio output of 
an f.m. receiver? 

2.19. An f.m. transmitter has a frequency swing of 80 kHz. Deter- 
mine its frequency deviation when the modulating signal vol- 
tage is halved. 

2.20. Explain why frequency modulation is not employed for 
medium-wave sound broadcasting. 


Modulators and 


Any radio system must operate in the frequency band that has 
been allocated to it. This means that the modulating, or 
baseband, signal must be frequency translated to a different 
part of the frequency spectrum. The translation process is 
carried out in the radio transmitter by modulating, either in 
amplitude or in frequency, a carrier wave of appropriate 
frequency. In the radio receiver the reverse process must be 
carried out, i.e. the signal must be demodulated. In this 
chapter the operation of the more commonly used modulators, 
excepting those using Class C power amplifiers, and demod- 
ulators will be considered. 

Amplitude Modulators 

The modulator circuits used in d.s.b radio transmitters must 
permit the modulating signal to amplitude modulate the car- 
rier wave without the production of an excessive number of 
extra, unwanted frequencies. The modulator used in an s.s.b. 
system must, in addition, also suppress the carrier frequency 
and, in some cases, the modulating signal also. 

D.S.B. Modulators 

The majority of d.s.b. amplitude-modulated radio transmitters 
use an anode- or collector-modulated Class C r.f . tuned power 
amplifier circuit and these will be discussed in Chapter 7. 

Other d.s.b. modulators utilize the non-linear relationship 
between applied voltage and resulting current of many elec- 
tronic devices. If a carrier wave at frequency f c and a sinusoi- 
dal modulating signal at frequency f m are applied in series to a 
non-linear device, the resultant current will contain compo- 



Fig. 3.1 D.S.B. 

amplitude mod- 

nents at various frequencies. Amongst these are components 
at the carrier frequency f c and the sum and difference frequen- 
cies f c ±/ m . If these components are selected, and all others are 
rejected, by means of a parallel-tuned circuit, an amplitude- 
modulated wave will be obtained. The non-linear device can 
be a diode but is more likely to be a suitably biased bipolar or 
field-effect transistor. 


One possible transistor modulator circuit is shown in Fig. 
3.1. The transistor is biased to operate over the non-linear 
part of its mutual characteristics. The carrier and modulating 
signal voltages are introduced into the base/emitter circuit of 
T 1 by means of transformers TRj and TR 2 respectively. The 
collector current contains the wanted carrier and sidefre- 
quency components plus various other, unwanted compo- 
nents. The collector circuit is tuned to the carrier frequency 
and has a selectivity characteristic such that the required 
amplitude modulated waveform appears across it. The various 
unwanted components are at frequencies well removed from 
resonance and do not develop a voltage across the collector 
load. The use of a non-linear modulator is restricted to low- 
power applications because the method has the disadvantages 
of low efficiency and a high percentage distortion level. 

S.S.B. Modulators 

In an s.s.b. or an i.s.b. system the carrier component is 
suppressed during the modulation process by using a balanced 
modulator. When a low-level pilot carrier is transmitted, it is 
added to the s.s.b.s.c. signal at a later point in the transmitter. 

The circuit of a transistor balanced modulator is given in 
Fig. 3.2. Transistors T x and T 2 are biased to operate on the 
non-linear part of their characteristics. Since the input trans- 


Fig. 3.2 Transistor balanced mod- 

former TRi is centre-tapped, the modulating signal voltages 
applied to transistors T l and T 2 are in antiphase with one 
another. The carrier voltage is introduced into the circuit 
between the centre-tap on the input transformer and earth, 
and so applies in-phase voltages to the two transistors. The 
collector currents of each transistor contain components at a 
number of different frequencies, and flow in opposite direc- 

(no carrier) 

tions in the primary winding of the output transformer TR 2 . 
The phase relationships of the various components of the 
collector currents are such that the current flowing in the 
secondary winding of TR 2 contains components at the mod- 
ulating frequency and at the upper and lower sidefrequencies 
but not at the carrier frequency. In practice, the two halves of 
the circuit do not have identical characteristics and some 
carrier leak is always present at the output of the circuit. 

Many balanced modulators, particularly those employed in 
multichannel line systems, do not utilize the square-law 
characteristics of a diode or transistor but instead use the 
device as an electronic switch. When a diode or transistor is 
forward biased its resistance is low, and when it is reverse 
biased its resistance is high. Provided the carrier voltage is 
considerably greater than the modulating signal voltage, the 
carrier will control the switching of the device. Ideally, a 
device should have zero forward resistance and infinite reverse 
impedance, and this will be assumed in the circuits that follow. 


Modulating ; 


(no carrier) 




Fig. 3.3 Single balanced modulator 

Modulating '. 


Fig. 3.4 Operation of a single bal- 
anced modulator 


12 3 4 


Fig. 3.B Output waveform of a 
single balanced modulator: (a) mod- 
ulating signal, (b) carrier wave, (c) 
output waveform 

(1) Fig. 3.3 shows the circuit of a SINGLE-BALANCED 
DIODE MODULATOR. During the half -cycles of the carrier 
waveform that make point A positive with respect to point B, 
diodes Dj and D 2 are forward biased and have zero resistance. 
The modulator may then be redrawn as shown in Fig. 3.4a; 
obviously the modulating signal will appear at the output 
terminals of the circuit. Similarly, when point B is taken 
positive relative to point A, the diodes are reverse biased and 
Fig. 3.4b represents the modulator. The action of the mod- 
ulator is to switch the modulating signal on and off at the 
output terminals of the circuit. The output waveform of the 
modulator can be deduced by considering the modulating 
signal and carrier waveforms at different instants. Consider 
Fig. 3.5: during the first positive half-cycle of the carrier wave 
a part of the modulating signal appears at the output (1-2 in 
Fig. 3.5c); in the following negative half-cycle the modulating 
signal is cut off (2-3); in the next positive half -cycle the 
corresponding part of the modulating signal again appears at 
the output terminals (3-4); and so on. 

Analysis of the output waveform shows that it contains the 
upper and lower sidefrequencies of the carrier (f c ±f m ), the 
modulating signal f m , and a number of higher, unwanted 
frequencies, but the carrier component is not present. In 
practice, of course, non-ideal diodes are employed and this has 
the effect of generating further unwanted frequencies and of 
reducing the amplitude of the wanted sidefrequency. Some 
carrier leak also occurs, and a potentiometer is often included 
to enable adjustment for minimum leak to be carried out. 



B Modulated 
(no carrier) 




Carrier signal 

Fig. 3.6 Cowan modulator 



Fig. 3.7 Operation of the Cowan 

(2) Anotner circuit that performs the same function is the 
COWAN MODULATOR (Fig. 3.6). The carrier voltage is 
applied across points A and B and switches the four diodes 
rapidly between their conducting and non-conducting states. 
When point B is positive with respect to point A, all four 
diodes are reverse biased and the modulator may be rep- 
resented by Fig. 3.7a; during the alternate carrier half -cycles 
Fig. 3.7ft applies. The modulator output therefore consists of 
the modulating signal switched on and off at the carrier 
frequency. The output waveform is the same as that of the 
previous circuit (Fig. 3.5) and contains the same frequency 
components. The Cowan modulator, however, does not re- 
quire centre-tapped transformers and it is therefore cheaper. It 
also possesses a self-limiting characteristic (i.e. the sidefre- 
quency output voltage is proportional to the input signal level 
only up to a certain value and thereafter remains more or less 




D 2 
Carrier signal 

Fig. 3.8 Ring modulator 

2 aL v nI J 

m "5 


Fig. 3.10 Output 
ring modulator: 
signal, (b) carrier 

waveform of the 

(a) modulating 

wave, (c) output 



(no carrier or 

modulated signal) 






Fig. 3.9 Operation of the ring mod- 

(3) Sometimes it is necessary to suppress the modulating 
signal as well as the carrier wave during the modulation 
process, and then a DOUBLE BALANCED MODULATOR 
is used. Fig. 3.8 shows the circuit of a ring modulator. During 
half -cycles of the carrier wave when point A is positive relative 
to point B, diodes D t and D 2 are conducting and diodes D 3 
and D 4 are not; D x and D 2 therefore have zero resistance and 
D 3 and D 4 have infinite resistance; Fig. 3.9a applies. Whenever 
point B is positive with respect to point A, diodes D x and D 2 
are non-conducting, D 3 and D 4 are conducting, and Fig. 3.9b 
represents the modulator. It is evident that the direction of the 
modulating signal current at the modulator output terminals 
is continually reversed at the carrier frequency. 

The output waveform of a ring modulator is shown in Fig. 
3.10c and can be deduced from Figs. 3.10a, b. Whenever the 
carrier voltage is positive, the modulating signal appears at the 
modulator output with the same polarity as a (see points 1-2 
and 3-4 at c). Whenever the carrier voltage is negative the 
polarity of the modulating signal is reversed (points 2-3 and 

Analysis of the output waveform shows the presence of 
components at the upper and lower sidefrequencies of the 
carrier wave and a number of higher, unwanted frequencies. 
Both the carrier and the modulating signal are suppressed. 

(4) The balanced modulator is also available in integrated 
circuit form. Besides the usual advantages of integrated cir- 
cuits over discrete circuitry, the i.e. modulators also offer 
exceptionally good carrier suppression, fully balanced input 
and output circuits, and are capable of operation over a wide 


Carrier fo 
input \o- 

Modulating /<> 
signal |o 

Fig. 3.11 Integrated balanced modulator 

frequency band, typically up to about 100 MHz. Fig. 3.11 
shows the basic circuit of an INTEGRATED DOUBLE- 
BALANCED MODULATOR. The variable resistor Rj is 
provided for adjustment of the carrier leak appearing at the 
output terminals to a minimum value. R 2 is a bias component 
and capacitors C x and C 2 decouple the positive and negative 
power supply lines. 

When a complex modulating signal is applied to any of the 
modulator circuits described, upper and lower sidebands are 
produced. In an s.s.b.s.c. system only one of the sidebands is to 
be transmitted and the other is to be suppressed. Two methods 
of sideband suppression are available, known respectively as 
the filter method and the phasing method. 

Sideband Suppression 

THE FILTER METHOD The more commonly used method 
of removing the unwanted sideband is to pass the output of the 
balanced modulator through a band-pass filter as shown in Fig. 
3.12. When the modulating signal frequency is close to the 
wanted sideband, the filter may not be able to provide suffi- 
cient rejection. When this is the case a double-balanced mod- 
ulator is used so that the modulating signal will not appear at 
the input terminals of the filter. 

Fig. 3.12 Filter method of produc- 
ing an s.s.b.s.c. signal 


fc*f m 





4, " 







The filter is required to have a flat attenuation characteristic 
in the passband and a rapidly increasing attenuation outside. 
The filter may be of inductor/capacitor construction or be of 
the crystal type. 

THE PHASE SHIFT METHOD The phasing method of 
generating an s.s.b.s.c. signal avoids the use of a filter at the 
expense of requiring an extra balanced modulator and two 
phase-shifting circuits. The block schematic diagram of the 

Fig. 3.13 Phasing method of pro- 
ducing an s.s.b.s.c. signal 


modulator 1 

90° phase- 





signal f m 



90° phase- 

modulator 2 



phasing method is given in Fig. 3.13. Balanced modulator 1 
has the modulating signal at frequency f m applied to it, to- 
gether with the output of the carrier-generating oscillator after 
it has been passed through a network which introduces a 90° 
phase lead. The other balanced modulator (2) has the carrier 
voltage applied directly to it but the modulating signal is first 
passed through a circuit which advances all frequencies by 90°. 
The result of the phase shifts given to the carrier and modulat- 
ing signals in different parts of the circuit is that the upper 
sideband outputs of the two modulators are in phase, but the 
lower sideband outputs are in antiphase. The modulator out- 
puts are combined in an additive circuit with the result that the 
lower sidebands cancel to leave a single sideband suppressed- 
carrier signal. 

If the lower sideband is to be transmitted instead of the 
upper sideband, the phasing of the circuit must be altered so 
that the phase-shifted signal and carrier voltages are both 
applied to the same modulator. Then the upper sidebands 
cancel. The phasing system of s.s.b.s.c. a.m. generation has 
some advantages over the filter method. Firstly, since a filter is 
not used, the method will operate at higher frequencies and, 
secondly, it is easy to switch from transmitting one sideband to 
transmitting the other sideband. The disadvantage of the sys- 
tem is the need for a network that can introduce 90° phase 
shift over the whole of the audio-frequency band. 


Frequency Modulators 

The function of a frequency modulator is to vary the frequency 
of the carrier in accordance with the characteristics of the 
modulating signal applied to it. There are two fundamentally 
different approaches to the problem. The frequency of an 
inductor-capacitor oscillator can be modulated by varying the 
capacitance or the inductance of its frequency-determining 
tuned circuit. Alternatively, a crystal oscillator can be phase- 
modulated in such a way that a frequency-modulated wave is 









Fig. 3.14 The principle of a fre- 
quency modulator 

Fig. 3.15 Transistor reactance mod- 

Direct Frequency Modulation 

The basic principle upon which the operation of all direct 
frequency modulators is based is shown in Fig. 3.14. A circuit 
whose reactance, generally capacitive, can be controlled by the 
modulating signal is connected in parallel with the frequency- 
determining tuned-circuit Lj-Q of the oscillator. When the 
modulating signal voltage is zero, the effective capacitance C e 
of the variable-reactance circuit is such that the oscillation 
frequency is equal to the nominal (unmodulated) carrier fre- 
quency, i.e. 

f osc = 1/2 WLLxCQ + C e )] Hz 

When the modulating signal is applied, the effective capaci- 
tance of the reactance circuit will be varied and this, in turn, 
will frequency-modulate the oscillator. Most direct frequency 
modulators are either some form of reactance frequency mod- 
ulator or a varactor diode modulator. 

(1) The circuit of a TRANSISTOR REACTANCE MOD- 
ULATOR is shown in Fig. 3.15. Resistors R lf R 2 , R 3 and 
capacitor Q are the usual bias and decoupling components. 
Capacitor C 3 is a d.c. blocking component which is necessary 
to prevent L 2 shorting the d.c. collector potential of T 1 to 
earth. Inductor L x is a radio-frequency choke. The output 

Oscillator tuned circuit 

"y *y c j L> 



impedance of the circuit is the ratio voltage/current at the 
terminals AA', and for this to be a capacitive reactance the 
current must lead the voltage by 90°. This is the purpose of the 
components R 4 and C 2 ; their values are chosen so that the 
voltage developed across i? 4 makes T r conduct an alternating 
current that leads the collector voltage by very nearly the 
required 90°. 

Frequency modulation of the oscillator frequency requires 
that the effective capacitance of the circuit is varied by the 
modulating signal. Since the capacitance is directly propor- 
tional to the mutual conductance of the transistor, it can be 
varied by applying the modulating signal to the base of T t . The 
impedance shunted across the oscillator tuned circuit by the 
modulator will have a resistive component also, and this will 
lead to some unwanted amplitude modulation of the oscillator. 
Often this amplitude modulation is small and can be tolerated. 
If it cannot, a limiter will have to be used to remove the 
amplitude variations. 

(2) An alternative method of frequency modulation is to con- 
nect a varactor, or voltage-variable diode in parallel with the 
tuned circuit of the oscillator. The capacitance of a varactor 
diode is a function of the reverse-biased voltage applied across 
it and can therefore be varied by the modulating signal. It is 
necessary for the oscillator frequency to be varied either side 
of its unmodulated value and so the varactor diode must have 
a mean capacitance value established by a bias voltage. 

Fig. 3.16 Varactor diode modulator 

tuned circuit 

9 9 

C 2 L 2 

-II— r 

cii "i: 


Bias voltage 


The basic circuit of a VARACTOR DIODE MOD- 
ULATOR is shown in Fig. 3.16. The diode Dj is connected in 
parallel with the oscillator tuned circuit Q-Lj. Capacitor C 2 is 
merely a d.c. block and L 2 is a radio-frequency choke to 
prevent oscillation frequency currents reaching the modulating 
signal circuitry. With no modulating signal the diode is reverse 
biased by the bias voltage V B and provides the capacitance C d 
necessary to tune the oscillator to the required unmodulated 
carrier frequency, Le. 


/ osc = l/2W[L(C 1 + Q)]Hz 


When the modulating signal is applied, a voltage V m sin a) m t 
appears across inductor L 4 and the total voltage applied to the 
diode is 

— V B + V m sin co m t volts 

This voltage varies the diode capacitance and in so doing 
frequency modulates the oscillator. 


(a) A variable capacitance diode has a characteristic given by Table 
3.1. Plot a graph of diode capacitance against diode voltage. 

Table 3.1 

Reverse voltage (V) -1 -2 -3 -4 -5 -6 

Diode capacitance (pF) 12.5 7.5 6.0 5.0 4.3 3.8 

(fc) A 90 MHz oscillator employs a parallel-tuned circuit to control 
the frequency of oscillation. The circuit consists of a coil of induc- 
tance 0.2 n H in parallel with a 10 pF capacitor, across which is 
connected the variable-capacitance diode described in (a) above. 
Using the given characteristic, determine the voltage which must be 
applied to the diode for oscillations to occur at 90 MHz 

(C &G) 


(a) The required graph is given in Fig. 3.17. 

Fig. 3.17 

12 - 

Bias voltage 


(b) The total capacitance needed to tune the inductance to resonance 
at 90 MHz is 

C, = 1/(4tt 2 x 90 2 x 10 12 x 0.2 x 10" 6 ) = 15.63 pF 

Therefore, the diode must provide a capacitance of 5.63 pF. From the 
graph of Fig. 3.17 this capacitance value is obtained when the applied 
voltage is —3.3 V. (Ans.) 

Indirect Frequency Modulation 

Direct frequency modulation of an oscillator has one main 
disadvantage. Since an inductor/capacitor oscillator must be 
used, the inherent frequency stability of the unmodulated 
carrier frequency is not high enough to meet modern require- 
ments. There are two possible solutions to this problem. Firstly 
a direct modulation system can be used and automatic fre- 
quency control applied to the transmitter or, secondly, a crystal 
oscillator can be used. With the second solution, an indirect 
method of modulation must be used since the frequency of a 
crystal oscillator cannot be varied. 

The phase deviation of a frequency-modulated signal is 
proportional to the amplitude of the modulating signal and 
inversely proportional to the modulating frequency. The phase 
deviation of a phase-modulated signal is proportional to the 
modulating signal voltage only. The relationships mean that if 
the modulating signal is integrated and is then used to phase 
modulate a carrier wave a frequency -modulated waveform is 






Fig. 3.18 Use of a phase modulator 
to generate a frequency-modulated 

obtained. The arrangement is shown in block schematic form 
in Fig. 3.18. 

One type of phase modulator that has enjoyed considerable 
popularity is the ARMSTRONG CIRCUIT shown in Fig. 
3.19. The output voltage of the balanced modulator contains 




90° phase- 
shifting circuit 




Fig. 3.19 The Armstrong phase 






the upper and lower sidebands produced by amplitude mod- 
ulating the 90° phase-shifted carrier with the modulating 
signal. The s.s.b.s.c. amplitude-modulated signal is then added 
to the zero-phase-shifted carrier component, to produce a 
phase-modulated signal. If the modulating signal is integrated 
before it arrives at the balanced modulator, a frequency- 
modulated output is produced. The frequency deviation pro- 
duced is very small, being usually of the order of about 30 Hz. 
Many alternative phase modulator circuits have been in- 
vented but mention will only be made of one of them. Phase- 
modulation of a carrier wave can be achieved by amplifying 
the carrier in a tuned amplifier whose collector load imped- 
ance is varied by the modulating signal. The principle of the 
method is illustrated by Fig. 3.20. When the modulating signal 




Fig. 3.20 Phase modulator 







voltage is zero the collector tuned circuit C l -L 1 is resonant at 
the crystal oscillator frequency. With the modulating signal 
applied, the total effective capacitance of the tuned circuit is 
varied and the circuit is de-tuned above and below resonance. 
This makes the phase of the output voltage alternately lag and 
lead the phase of the unmodulated output voltage, i.e. the 
output voltage is phase modulated. 

Amplitude Demodulators 

Demodulation or detection is the process of recovering the 
information carried by a modulated wave. The majority of 
d.s.b. amplitude-modulation sound broadcast receivers employ 
the diode detector, although increasingly the detection stage is 
included within an integrated circuit and then another kind of 
detector circuit is used. Many communication receivers oper- 
ate with either s.s.b or i.s.b. signals and use some form of 
product detector. 


The Diode Detector 

llitllrlp- r-Li 





Fig. 3.21 Diode detector circuit 



Input signal 

Fig. 3.22 Output voltage of a diode 
detector handling a signal of con- 
stant amplitude 

Fig. 3.21 shows the circuit of a diode detector, consisting of a 
diode in series with a parallel resistor-capacitor network. 

If an unmodulated carrier wave of constant amplitude is 
applied to the detector, the first positive half-cycle of the wave 
will cause the diode to conduct. The diode current will charge 
the capacitor to a voltage that is slightly less than the peak 
value of the input signal (slightly less because of a small 
voltage drop in the diode itself). At the end of this first 
half-cycle, the diode ceases to conduct and the capacitor starts 
to discharge through the load resistor R at a rate determined 
by the time constant, CR seconds, of the discharge circuit. 

The time constant is chosen to ensure that the capacitor has 
not discharged very much before the next positive half-cycle of 
the input signal arrives to recharge the capacitor (see Fig. 
3.22). The time constant for the charging of the capacitor is 
equal to Or seconds, where r is the forward resistance of the 
diode and is much less than R. A nearly constant d.c. voltage 
is developed across the load resistor R; the fluctuations that 
exist are small and take place at the frequency of the input 
carrier signal. 

If now the input signal is amplitude-modulated, the voltage 
across the diode load will vary in sympathy with the wave 
envelope, provided the time constant is small enough. The 
capacitor must be able to discharge rapidly enough for the 
voltage across it to follow those parts of the modulation cycle 
when the modulation envelope is decreasing in amplitude (see 
Fig. 3.23). The capacitor voltage falls until a positive half-cycle 
of the input signal makes the diode conduct and recharge the 
capacitor. When the modulation envelope is decreasing, one 
positive half-cycle is of lower peak value than the preceding 
positive half-cycle and the capacitor is recharged to a smaller 

Fig. 3.23 Output voltage of a diode 
detector handling an amplitude- 
modulated signal 


voltage Time constant 

too long 

Input signal 



c 1± 


c 2 

R 2 




— o 

Fig. 3.24 


Diode detector filter 

voltage. If the time constant of the discharge path is too long, 
relative to the periodic time of the modulating signal, the 
capacitor voltage will not be able to follow the troughs of the 
modulation envelope; that is, the decay curve passes right over 
the top of one or more input voltage peaks as shown by the 
dotted line in Fig. 3.23, and waveform distortion takes place. 

The time constant must not be too short, however, or the 
voltage across the load resistor will not be as large as it could 
be, because insufficient charge will be stored between succes- 
sive pulses of diode current. The time constant determines the 
rapidity with which the detected voltage can change, and must 
be long compared with the periodic time of the carrier wave 
and short compared with the periodic time of the modulating 

The voltage developed across the diode load resistor has 
three components: (a) a component at the wanted modulating 
signal frequency, (b) a d.c. component that is proportional to 
the peak value of the unmodulated wave (this component is 
not wanted for detection and must be prevented from reaching 
the following audio-frequency amplifier stage), and (c) compo- 
nents at the carrier frequency and harmonics of the carrier 
frequency that must also be prevented from reaching the 
audio-frequency amplifier. To eliminate the unwanted compo- 
nents the detector output is fed into a resistance-capacitance 
filter network before application to the audio-frequency amp- 

Fig. 3.24 shows a possible filter circuit. Capacitor C 2 acts as 
a d.c. blocker to remove the d.c. component of the voltage 
appearing across load resistor jRj. Capacitor C 3 has a low 
reactance at the carrier frequency and its harmonics and, in 
conjunction with resistor R 2 , filters out voltages at these 
frequencies. The voltage appearing across R 3 is therefore just 
the required modulating signal. 


Fig. 3.25 Another diode detector °~ 
filter circuit 

Ic 2 

"2 ^3^ "3 

T I T 



— o 

An alternative arrangement is shown in Fig. 3.25. Capacitor 
C 2 is the d.c. blocker and C 3 -R 3 is the r.f. filter; R 3 also 
functions as the volume control. 





pC 4 


1 II o 

Fig. 3.26 The transistor detector 

The Transistor Detector 

The circuit of a common-emitter transistor detector is shown in 
Fig. 3.26. Rectification takes place in the emitter/base circuit 
and the rectified signal is amplified by the transistor in the 
usual way. 

Components R u R 2 , -R 4 , C 2 and C 3 provide bias and d.c. 
stabilization and R 3 is the collector load resistor. C 4 is a 
by-pass capacitor to prevent voltages at the carrier frequency 
appearing across R 3 and being fed, via C 5 , to the output 
terminals of the circuit. 

The input amplitude-modulated signal is fed into the 
base/emitter circuit via r.f. transformer TR 1; the primary wind- 
ing of which is tuned to the carrier frequency. The 
base/emitter junction of transistor T 1 acts as a semiconductor 
diode and together with R 2 and C 2 forms a diode detector. 
The detected voltage appears across R 2 and varies the 
emitter/base bias voltage of the transistor. This variation 
causes the collector current to vary in accordance with the 
modulation envelope. A voltage at the modulating signal fre- 
quency appears across the collector load resistor R 3 and this is 
coupled to the load by capacitor C s . 

The disadvantage of the transistor detector is its limited 
dynamic range and for this reason it is not often used in 
broadcast receivers having discrete circuitry. The circuit is 
used in the detector section of some integrated circuits. 

The Balanced Demodulator 

Demodulation of an s.s.b or an i.s.b. signal can be achieved 
with any of the balanced modulators previously discussed. The 
carrier component which was suppressed at the transmitter 
must be re-inserted at the same frequency and the input or 
modulating signal is the transmitted sideband. 







Fig. 3.27 Use of a balanced mod- 
ulator as a demodulator 


Suppose that the modulating signal is a sine wave of fre- 
quency f m and that the lower sideband is transmitted. Then the 
input to the demodulator is at frequency f c -f m and the 
demodulator output contains components at frequencies f c ± 
(f c -f m ). The lower sidefrequency is selected by a low-pass 
filter and is equal to f c -(f c -f m ), or f m , which is the required 
modulating signal (see Fig. 3.27). 

The frequency of the re-inserted carrier must be very close 
to the frequency of the carrier which was suppressed at the 
transmitter. Otherwise the frequency components of the de- 
modulated output waveform will bear the wrong relationships 
to one another. The maximum permissible frequency error 
depends upon the nature of the signal. It may be as large 
as ±15 Hz for speech transmissions but only 2 Hz for 
telegraphy/data signals. As in the case of the modulator it is 
essential for the carrier amplitude to be considerably larger 
than the signal amplitude to ensure that the diodes are 
switched by the carrier. When digital data is being received, it 
is necessary for the re-inserted carrier to also be phase- 

Another method of demodulating an s.s.b. signal is known as 
the PRODUCT DETECTOR, two versions of which are 
shown in Fig. 3.28a and b. In both of these circuits the a.c. 
current conducted by the active device is proportional to the 
product of the s.s.b.s.c. and carrier voltages. The output cur- 
rent therefore contains components at a number of different 
frequencies amongst which is a component at the difference 
frequency. Assuming sinusoidal modulation this is equal to 
fc~ifc~fm) or fm ; thus the difference frequency is the required 
modulating signal. In both circuits, higher frequency unwanted 
components are filtered out by the shunt capacitor C 3 . 

-E +V 


1 J Audio _ . ■ J 

T T C2 signal c, ™ r T t T 

Carrier X~ s.s.b.s.c. 

voltage T 3 signal I I I 

_J x L_ I x—x — 





Fig. 3.28 Two product detectors 



The product detector, also known as the heterodyne detec- 
tor, is increasingly used in modern circuitry. It is particularly 
convenient for implementation in integrated circuit form, al- 
though normally within a package that also provides other 
circuit functions, such as i.f. amplification. The product de- 
modulator is also capable of detecting d.s.b. signals but usually 
only the i.e. versions are used for this purpose. 

Frequency Demodulators 

The function of a frequency demodulator is to produce an 
output voltage whose magnitude is dnectly^proportiojiaLto the 
frequency deviation ofthe input signal, and whose frequency is 
equal to the number of times per" second the input signal 
frequency is varied about its mean value. Frequency demod- 
ulation can be achieved in several different ways. Most receiv- 
ers using discrete circuitry employ either the ratio detector or 
the Fos ter-Se eley discriminator, but receivers incorporating 
integrated circuitry often use either the quadrature detector or 
a phase-locked loop. 

Fig. 3.29 Foster-Seeley detector 

The Foster-Seeley Discriminator 

The circuit diagram of a Foster-Seeley discriminator is given in 
Fig. 3.29. The tuned circuit C^L^ acts as the collector load for 
the final stage of the i.f. amplifier, which is generally operated 

+ 5* 

c 1± 




i — r 

T C 4 

I 1 

T C 5 


a.f. output 

^C e 


as a limiter. Both tuned circuits C t -Li and L 2 -C 3 are tuned to 
resonate at the unmodulated carrier frequency and have band- 
widths wide enough to cover the rated system deviation of the 
f.m. signal. Capacitors C 2 , C 4 and C 5 all have negligible 
reactance at radio frequencies and so L x is effectively con- 
nected in parallel with L 3 . Thus the voltage V x developed 
across L x also appears across L 3 . 

Suppose the voltage appearing across L t is at the unmod- 
ulated carrier frequency. The current flowing in L x induces an 




e.m.f. into the secondary winding L 2 and this causes an in- 
phase current to flow in the series circuit L2-C3. A voltage is 
developed across C 3 which lags this current, and hence the 
induced voltage by 90°. Since inductor L 2 is accurately centre- 
tapped, one-half of this voltage appears across each half of L 2 . 

Let the voltage appearing across the upper half of the 
winding be labelled as V 2 with V 3 being the voltage across the 
lower half. The total voltages V D1 and V D2 applied across the 
diodes Di and D 2 are, respectively, the phasor sums of the 
voltages Vi and V 2 , and V x and V 3 . The phase relationships 
are such that V 2 leads V x by 90° and V 3 lags V t by 90° as 
shown by the phasor diagram of Fig. 3.30a. Since V D1 = V D2 , 
equal amplitude detected voltages appear across the diode 
load resistors R t and R 2 . Because of the diode connections, 
these two voltages act in opposite directions and cancel out, so 
that the voltage appearing across the output terminals of the 
circuit is zero. 

When the frequency of the signal voltage developed across 
L x is above the unmodulated carrier frequency, the voltage 
across C 3 will lead the e.m.f. induced into L 2 by some angle 
greater than 90°. This results in V 2 leading V t by an angle less 
than 90° and V 3 lagging V t by more than 90° (Fig. 3.30&). 
Now the voltage V D1 applied across diode D t is larger than 
the voltage V D2 applied to D 2 and so the voltage developed 
across load resistor J?i is greater than the voltage across R 2 . A 
positive voltage, equal to the difference between the two load 
voltages, is produced at the output terminals. If the frequency v 
deviation of the carrier is increased, the larger will become the 
difference between the magnitudes of the diode voltages V D1 
and V D2 , and the output voltage will increase in the positive 


When the modulated frequency is below its mean value, 
voltage V 2 leads V t by more than 90°, while V 3 lags Vj by less 
than 90° as shown in Fig. 3.30c. As a result, V D2 is now of 
greater magnitude than V D1 and the detected voltage across 
R 2 is bigger than the voltage across i?,. The output voltage of 
the circuit is now negative with respect to earth. As before, an 
increase in the frequency deviation of the carrier will increase 
the output voltage. 

The way in which the output voltage of the circuit varies as 
the frequency of the input signal is changed is shown by the 
typical discriminator characteristic of Fig. 3.31. 

£ +2 

+1 - 

Fig. 3.31 Output voltage/frequency 
characteristic of a Foster-Seeley 

-1 - 

100 +125 

Frequency (kHz) 
off- tune from 

(unmodulated carrier 


Operation of the detector should be restricted to the linear 
part of the characteristic. The turn-over points are produced 
by the limited bandwidth of the tuned circuits C^-L^ and 
C 3 -L 2 , reducing the voltages applied to the diodes. 

The output voltage of the circuit will also vary if the 
amplitude of the input signal should vary. This is, of course, an 
undesirable effect and to prevent it happening the detector 
should be preceeded by one or more stages of amplitude 
limiting. De-emphasis of the output signal is provided by R 3 
and C 6 . 


Fig. 3.32 The ratio detector 

The Ratio Detector 

A commonly used f.m. detector, particularly for broadcast 
receivers, is the ratio detector, one form of which is given by 
Fig. 3.32. The main advantage of this circuit over the Foster- 
Seeley detector is that it incorporates its own amplitude limiting 
action and often a separate limiter is not needed. 

oa.f. output 

Inductor L x is inductively coupled to both L 2 and L 3 but L 2 
and L 3 are not coupled together. The tuned circuits C^^ and 
C3-L3 are each tuned to the unmodulated carrier frequency. 
When a voltage at this frequency appears across L 1; voltages 
are induced into both L 2 and L 3 . Capacitors C 2 , C 4 and C 5 
have negligible reactance at radio frequencies and so the 
voltage applied across diode Dj is the phasor sum of the 
voltages across L 2 and the upper half of L 3 . Similarly the 
voltage applied to D 2 is the phasor sum of the voltages across 
L 2 and the lower half of L 3 . If the voltage across L 2 is labelled 
as V t and the other two voltages are labelled V 2 and V 3 
respectively, the phasor diagram given in Fig. 3.30 will repre- 
sent the voltages. The resultant voltages V D1 and V D2 applied 
to the diodes will vary with frequency to produce voltages 
across the load capacitors C 4 and C s . The voltage across the 
d.c. load capacitor C 7 is the sum of the voltages across C 4 and 
C 5 and, since R 2 = R 3 , one-half of this voltage appears across 
each resistor. The time constant C 7 {R 2 + R3) is sufficiently long 
to ensure that the voltage across C 7 remains more or less 
constant at very nearly the peak voltage appearing across C 3 . 

The audio load capacitor C 2 is connected between the 
junctions of CJC 5 and R 2 /R 3 , and this part of the circuit is 
re-drawn in Fig. 3.33. The voltages across C 5 and R 3 have the 


Fig. 3.33 

polarities shown and, when the input signal is at the unmod- 
ulated carrier frequency, are of equal magnitude. The two 
voltages act in opposite directions, with the result that no 
current flows, and the voltage across the audio load capacitor 
C 2 is zero. When the input signal frequency increases, the 
voltage applied to diode Di increases and the voltage across 
D 2 falls. As a result the voltage across C 4 increases while the 
voltage across C s falls; but, since the sum of these voltages 
remains constant, the voltage across R 3 does not change. A 
current now flows in the circuit of Fig. 3.33 and a positive 
voltage, equal to the difference between V C5 and Vr 3 , appears 
across C 2 . If the frequency deviation is increased, the voltage 
across C 5 will fall still further and the voltage across C 2 will 
increase. Conversely, if the input frequency is reduced, the 
voltage across C 5 will become bigger than the voltage 
across R 3 , and a current will flow in the opposite direction to 
before to produce a negative output voltage. When the fre- 
quency of the input signal voltage is modulated, the modulat- 
ing signal voltage will appear across C 2 . Components R r and 
C 6 provide de-emphasis of the output voltage. 

The output-voltage/input-frequency characteristic of a ratio 
detector has the same shape as the Foster-Seeley curve shown 
in Fig. 3.31. However, the output voltage available for a given 
frequency deviation is only one-half that provided by the 
Foster-Seeley circuit, and the linearity of the characteristic is 
not as good. The advantage of the ratio detector has been 
previously mentioned; it provides some degree of self -limiting 
in the following manner. If the amplitude of the input signal is 
steady, the voltage across the d.c. load capacitor C 7 is constant 
because of the long time constant C 7 (R 2 + R 3 ). An increase in 
the input signal voltage will cause both diodes to conduct extra 
current, and this results in an increased volts drop across the 
tuned circuit, tending to keep the voltage applied to the diodes 
more or less constant. A similar action takes place if the input 
signal voltage should fall; the diodes pass a smaller current and 
the volts drop across the tuned circuit is reduced, allowing the 
diode voltage to rise. The variable voltage drop across the 
tuned circuit in conjunction with the long time constant of the 
diode load ensure that the output voltage responds very little, 
if at all, to any changes in input signal amplitude. 

The ratio detector shown in Fig 3.32 is balanced since the 
d.c. voltage appearing across the d.c. load capacitor C 7 is 
balanced with respect to earth potential. Sometimes it is 
convenient to have an unbalanced voltage and then an unbal- 
anced circuit is used. Fig. 3.34 shows the circuit of one version 
of the unbalanced ratio detector; its operation is left as an 
exercise for the reader (see Exercise 3.14). 


Fig. 3.34 Unbalanced ratio detector 

O a.f. output 

The Quadrature Detector 

The action of a quadrature detector depends upon two vol- 
tages, which are both derived from the f.m. signal to be 
detected and which are 90° out of phase with one another at 
the unmodulated carrier frequency. Essentially, the detector 
compares the relative phases of the signal on either side of a 
single tuned circuit. Quadrature detection is rarely found in 
discrete form but is increasingly used in modern equipment 
since it is convenient for fabrication within an integrated 
circuit. Generally the i.e. includes an i.f. amplifier, a limiter, 
the quadrature detector, and, sometimes, an audio-frequency 
pre-amplifier. Two rectangular voltages, both derived from the 
f.m. signal to be demodulated, are applied to a transistor 
circuit which produces an output voltage only when both input 
voltages are present. At the unmodulated carrier frequency, 
the two input voltages have a time difference of a quarter of a 
period between them, corresponding to the 90° (quadrature) 
phase shift (Fig. 3.35a). When the frequency of the f.m. signal 
is above its umodulated value, voltage waveform b is advanced 
in time (Fig. 3.35b) and the pulses of output voltage occupy 
longer intervals of time. Conversely when the signal frequency 
is decreased, the pulses of output voltage are narrower (Fig. 
3.35c). The mean value of the output voltage is thus propor- 
tional to the frequency deviation of the input signal voltage. If 
the input signal is frequency modulated, the mean value of the 
output voltage will vary with the waveform of the modulating 

The quadrature detector is often used in i.e. form since all 
the necessary components except one can be fabricated within 
the chip. The exception is the quadrature coil which is required 
to produce the necessary time difference between voltages A 
and B. 


The Phase-locked Loop Detector 

Another method of f.m. detection which has only become an 
economic proposition since the advent of linear integrated 
circuits is the phase-locked loop (p.l.L), the block schematic 
diagram of which is shown in Fig. 3.36. 

If a signal at a constant frequency is applied to the input 
terminals of the circuit, the phase detector produces an output 
voltage that is proportional to the instantaneous phase differ- 
ence between the signal and oscillator voltages. The error 
voltage is filtered and amplified before it is applied to the input 
of the voltage-controlled oscillator. The error voltage varies 
the oscillator frequency in the direction which reduces the 
frequency difference between signal and oscillator. This action 
continues until the oscillator frequency is equal to the signal 
frequency. The oscillator is then said to be locked; in this 
condition a small phase difference will exist between the signal 
and oscillator voltages in order to generate the error voltage 
needed to maintain the lock. 

If the input signal frequency should change, the error vol- 
tage will change also, with the appropriate polarity, and force 
the oscillator frequency to follow. When the input signal is 
frequency modulated, the error voltage will vary in the same 
way as the required modulating signal and so the circuit acts as 
an f.m. demodulator. The circuit can be made using discrete 
components or using integrated operational amplifiers but 
most convenient is the integrated p.l.l. circuit. 

Fig. 3.37 shows the basic circuit of an integrated p.l.l. f.m. 
demodulator. CV and C 2 couple the previous stage in the radio 
receiver to the detector and C 3 is the tuning capacitor of the 
voltage-controlled oscillator. C 5 is a part of the low-pass filter 
between the phase detector and the amplifier, and lastly C 4 
and i?i are the de-emphasis components. 

The p.l.l. detector offers a number of advantages over its 
competitors, namely: (a) the detector is tuned to the unmod- 
ulated carrier frequency by a single external capacitor; (b) the 
upper-frequency limit is high; (c) it introduces little noise or 
distortion; and (d) it does not require an inductance. The 
circuitry is complicated and not competitive economically if 
discrete components are used. The integrated circuit versions 
also used to be expensive but their present cost is such that they 
are employed in some communication receivers. 


Voltage a 




n • • i. Mean voltage 
Output voltage — 

Voltage a 



Mean voltage 


Output voltage 


Voltage a 

Voltage b 

Output voltage 

Mean voltage 


Fig. 3.35 Operation of a quadrature detector (Note: mean voltage not 
drawn to scale) 

modulated signal 


Fig. 3.36 Phase-locked loop fre- 
quency detector 




a.f. output 

modulated signal 1 

Fig. 3.37 Integrated p.l.l. frequency 



3.1. (a) Explain how a ratio detector produces amplitude limiting. 
(b) With severe amplitude variations of the input signal the 
limiting action of a ratio detector may produce distortion of the 
output signal. Explain what causes this type of distortion and 
how the effect may be minimized. (C & G) 

3.2. Draw a block schematic diagram of a phase-locked loop 
frequency-modulation detector. Explain the principle of opera- 
tion of the circuit. What are the advantages of this type of 

3.3. (a) Draw the circuit diagram of a Foster-Seeley discriminator 
with an amplitude limiter preceding it. (b) Describe its opera- 
tion as an f.m. demodulator, (c) Which parts of your circuit 
control the bandwidth over which the discriminator operates? 


3.4. Fig. 3.38 shows a discriminator, (a) What type is it? Draw 
phasor diagrams relating Vj with each of V 2 , V 3 and V 4 when 
the signal is (i) at the carrier frequency, (ii) above the carrier 
frequency, (c) Draw a typical input/output characteristic for 
such a discriminator, labelling the axes, (d) What happens to 
the output if the incoming carrier drifts from its nominal fre- 

quency .' 


Fig. 3.38 




(a) Draw a circuit diagram of (i) a ratio detector, (ii) a Foster- 
Seeley discriminator, giving typical component values for a v.h.f . 
f.m. system with a 15 kHz output signal bandwidth, (b) Briefly 
discuss the limiting action of a ratio detector, (c) If the input 
signals are the same, what is the ratio between the a.f. outputs 
of the two types of demodulator mentioned in (a)? (d) What is 
the time constant for the Foster-Seeley discriminator you have 
drawn in (a)? (C & G) 

Describe briefly the principle of operation of each of the 
following kinds of f.m. detector: (a) phase discriminator, (t>) 
phase-locked loop, and (c) quadrature. Which of these detec- 
tors are best suited to implementation in integrated circuit 

Explain, with the aid of appropriate diagrams, how an s.s.b.s.c. 
signal can be produced (a) by the filter method and (b) by the 
phasing method. Compare the relative merits of the two 
methods. / 


3.8. Draw the circuit diagram of a diode detector suitable for the 
demodulation of d.s.b. amplitude-modulation signals. Explain 
the operation of the circuit and give typical component values. 

3.9. (a) What is a varactor diode? (b) Draw the circuit diagram of a 
varactor diode modulator and explain its operation, (c) At what 
stage in an f .m. transmitter is pre-emphasis applied? (d) Sketch 
a typical pre-emphasis characteristic, annotating the axes. 


3.10. Describe with circuit diagrams the function and operation in 
frequency modulation equipment of (a) a limiter, (b) a reac- 
tance modulator. (C & G) 

3.11. (a) Explain how the input-voltage/output-current characteristic 
of a semiconductor diode is used to demodulate an amplitude- 
modulated wave, (b) An amplitude-modulated signal is applied 
to the input of the diode detector shown in Fig. 3.24. By 
reference to current or voltage waveforms describe the function 
of each component in reproducing the modulating signal. 


3.12. Fig. 3.39 shows the pin connections of an integrated circuit 
double-balanced modulator. The pin functions are as listed: 
1 + signal in 8 + power supply voltage 
2— signal in 10+ output 
3+ carrier in 12— output 
4 decouple 13 carrier leak adjust 
7 + carrier in 14 earth. 

(a) Draw a suitable modulator circuit using this i.e. (b) List 
Fig. 3.39 the advantages of i.c.s over the use of discrete components. 

3.13. Explain, with the aid of block diagrams, how a frequency 
modulated wave can be produced using (a) a direct method and 

(b) an indirect method. Why is the indirect method employed? 

3.14. Explain, with the aid of phasor diagrams, the operation of the 
ratio detector circuit given in Fig. 3.34. 

Short Exercises 

3.15. Draw the circuit diagram of a balanced modulator that employs 
two junction field-effect transistors as the non-linear elements. 

3.16. Draw the block diagram of the phase-shifting method of pro- 
ducing an s.s.b.s.c. signal in which the upper sideband is trans- 

3.17. Should the bandwidth of the tuned circuits of a Foster-Seeley 
discriminator be greater or less than the rated system deviation 
of the signal to be detected? Give a reason for your answer. 

3.18. Draw the circuit diagram of a double-balanced demodulator 
using an integrated circuit. 

3.19. (a) What is the function of the modulator stage in a radio 
transmitter? (b) What is the function of the detector stage in a 
radio receiver? 

3.20. What are the requirements for the demodulation of an s.s.b.s.c. 
signal in terms of (a) the magnitude of the re-inserted carrier, 
(b) the frequency of the re-inserted carrier, and (c) the phase of 
the re-inserted carrier? 

3.21. Draw the circuit diagram of a reactance frequency modulator 
using a field-effect transistor. State which kind of f .e.t. you have 
















3.22. List the component frequencies which appear across the load 
resistor of a diode detector. Explain, with the aid of a diagram, 
how the unwanted components are removed before the de- 
tected signal is applied to the audio amplifier. 

3.23. A 2 kHz sinusoidal signal is applied to a balanced modulator 
along with a 80 kHz carrier wave and the lower sidefrequency 
is selected by a suitable filter. At the receiver the s.s.b.s.c. signal 
is applied to a balanced demodulator together with a carrier at 
80.045 kHz. Determine the frequency of the demodulated 

3.24. Fig. 3.40 shows the circuit of an integrated product detector. 
Suggest the function of each component shown. 

3.25. List the relative advantages and disadvantages of 

(a) a Foster-Seeley discriminator, a ratio detector, and a quad- 
rature detector. 

(b) a diode detector, a transistor detector, and a product 



input Cy 
o It 

Fig. 3.40 


Transmission Lines 


The basic purpose of a transmission line is to transmit electri- 
cal energy from one point to another. The length of a line may 
be several kilometres in the case of a line communication 
system, some tens or hundreds of metres in the case of a feeder 
used to connect a radio transmitter or receiver to its aerial, or 
perhaps only a fraction of a metre when the line is used as an 
integral part of a u.h.f . equipment. 

Essentially a transmission line consists of a pair of conduc- 
tors separated from one another by a dielectric. The two main 
types of line used in radio communication systems are the 
two-wire or twin line and the coaxial pair. Both types of cable 
are available with air as the dielectric, or with some insulating 
material such as polythene. Each conductor of a pair has both 
series resistance and inductance, and shunt capacitance and 
leakance exists between the conductors. The magnitudes of the 
four primary coefficients depend upon the physical dimensions 
of the conductors and the nature of the dielectric used. The 
values of the resistance and the leakance also depend upon the 
frequency of the signal propagating along the line. 

Matched Transmission Lines 

The behaviour of a transmission line when a signal is applied 
across its input terminals is determined by its secondary 
coefficients. The four secondary coefficients of a line are its 
characteristic impedance, its attenuation and phase-change 
coefficients, and its phase velocity of propagation. 





To infinity 







Fig. 4.1 

of a line 

Characteristic impedance 

Characteristic Impedance 

The characteristic impedance Z of a transmission line is the 
input impedance VJIs of the line when either the line is of 
infinite length or it is terminated in its characteristic impe- 
dance. The two definitions, illustrated by Fig. 4.1, are essen- 
tially the same as demonstrated in TSII. 

The characteristic impedance of a radio-frequency line is 
determined by the inductance and capacitance of the line in 
accordance with equation (4.1): 

Z = v / (L/C) ohms (4.1) 

The characteristic impedance of a particular r.f. line is of 
constant magnitude, since neither the inductance L nor the 
capacitance C varies with frequency, and is purely resistive. 
This means that at all points along the line the current and 
voltage are in phase with one another. 

In turn, the inductance and capacitance of a line depend 
upon its dimensions, such as conductor diameter and spacing 
and so therefore does the characteristic impedance. 

For a two-wire line 

^ 276 , D L 
Z = -7— log 10 — ohms 

Ve r r 


where D is the spacing between the centres of the two 
conductors, r is the radius of each conductor, and e r is the 
relative permittivity of the continuous dielectric. 
For a coaxial line 

rr 138 , R L 

Z = -7— log 10 — ohms 

vs. r 


where R is the inner radius of the outer conductor and r is the 
radius of the inner conductor. 

Because of constructional difficulties, such as the need to 
avoid very small conductor spacings, not all characteristic 
impedance values are available. For two-wire lines, Z is 
normally bigger than 100 ft and for coaxial lines Z is usually 
30-100 ft. 

Attenuation Coefficient 

As a current or voltage wave is propagated along a line, its 
amplitude is progressively reduced or attenuated, because of 
losses in the line. These losses are of three types: firstly there 
are conductor losses caused by PR power dissipation in the 
series resistance of the line; secondly there are dielectric 
losses; and thirdly, radiation losses. Radiation losses will occur 
in a balanced twin line at frequencies high enough for the 


conductor separation to be an appreciable fraction of the 
signal wavelength. Radiation loss does not occur in a coaxial 
pair in which the outer is made of solid copper, but some 
losses will take place when a braided outer is used. 

The radiation losses are difficult to determine but should be 
small if the correct type of cable is used. Neglecting the 
radiation losses, it is found that, if the current or voltage at the 
sending-end of the line is I s or V s , then the current or voltage 
one metre along the line is 

I^I.e-" or V 1 =V,e~ a 

where e is the base of natural logarithms (2.7183) and a is the 
ATTENUATION COEFFICIENT of the line in nepers per 
metre, where 1 neper = 8.686 dB. In the next metre length of 
line, the attenuation is the same and so the current I 2 , two 
metres along the line, is 

I 2 = j ie - = i s e-°e-"=J s e- 2 " 

Similarly V 2 =V s e~ 2a 

If the line is / metres in length, the current and voltage 
received at the outputs terminals of the line are given, respec- 
tively, by 

/r = / s e-' (4.4) 

V r = V s e-«' (4.5) 

Equations (4.4) and (4.5) show that both the current and 
voltage waves decay exponentially as they propagate along the 
length of the line. 

At radio frequencies the attenuation coefficient of a line is 
given by equation (4.6) 

a = R/2Z Q + GZJ2 nepers/metre (4.6) 

where R is the series resistance per metre loop and G is the 
leakance per metre. 

The attenuation coefficient is not a constant quantity but 
increases with increase in frequency. The two contributory 
parts of the attenuation coefficient vary with frequency in 
different ways; the conductor losses are proportional to the 
square root of frequency but the dielectric losses are directly 
proportional to frequency. Normally, the conductor losses are 
several times larger than the dielectric losses and often, par- 
ticularly with c oaxia l lines, the dielectric loss is small enough 
to be neglected! Then the line attenuation is proportional to 
the square root 'of frequency, while the signal wavelength is 
inversely proportional to frequency. This means that the at- 
tenuation per wavelength decreases with increase in frequency. 
Often, particularly at the v.h.f. and higher bands, the loss of a 
line is small enough to be neglected; then the line is usually \ 
described as being low -loss or loss -free. ^ — 1 


Phase Change Coefficient 

As a current or voltage wave travels along a line, it experi- 
ences a progressive phase lag relative to its phase at the 
sending-end of the line. The PHASE-CHANGE COEFFI- 
CIENT |8 of a line is the number of radians or degrees phase 
lag per metre. If, for example, /3 = 2° per metre, then a 10 
metre length would introduce a phase shift of 20°. At radio 
frequencies the phase change coefficient is given by equation 

(3 = <d\I{LC) radians/metre 


Clearly the phase change coefficient is directly proportional 
to frequency. At the higher frequencies, lines are often quoted 
in terms of their electrical length; this is the product (il 
expressed in wavelengths. 


A transmission line has a phase change coefficient /3 of 30° per metre 
at a particular frequency. If the physical length of the line is 1.5 m 
calculate its electrical length. 


£/ = 30° x 1.5 = 45° 
In one wavelength a phase shift of 360° takes place. Therefore, 

45 A 

Electrical length = T77-A = - 

360 8 


Phase Velocity of Propagation 

The phase velocity of propagation V p of a transmission line is 
the velocity with which a sinusoidal current or voltage wave is 
propagated along a line. Any sinusoidal wave travels with a 
velocity of one wavelength per cycle and since there are / 
cycles per second this corresponds to a velocity of Xf metres 
per second. Therefore, 

Vp = Xf metres/second 


where A is the wavelength and / is the frequency of the 
sinusoidal wave. 

In a distance of one wavelength a phase lag of 2 tt radians 
occurs and so 

j3 =2ttIX radians 


A = 2-7T//3 


V P =— -/=«V/3 (4.9) 


At radio-frequencies 

V p = w/w V(LC) = 1/V(LC) metres/second (4. 10) 

and has the same value at all frequencies. This means that all 
the component frequencies of a complex signal will propagate 
along a line at the same velocity and arrive at the end of the 
line together. Thus, the signal envelope will not suffer group 
delay/frequency distortion [TSII]. 

The phase velocity of propagation on a line is always some- 
what smaller than the velocity of light (c = 3xl0 8 m/s). 
Usually, the velocity is somewhere between 0.6 c and 0.9 c. 

Propagation on a Matched Line 

The input impedance of a matched line, that is one that is 
terminated in Z , is equal to Z . Suppose a generator of e.m.f. 
E s and impedance Z s is connected across the input terminals 
of the line. The voltage appearing across the terminals is then 

V S =E S ZJ(Z S + Z ) 

and the input current I s is equal to 

E S I(Z S + Z ) 

The input current and voltage propagate along the line and are 
attenuated and phase shifted as they travel. At any point along 
the line the ratio of the voltage and the current at that point is 
equal to the characteristic impedance Z . At the receiving end 
of the line, all the power carried by the waves is dissipated in 
the load impedance. 

Mismatched Transmission Lines 

Very often a transmission line is operated with a terminating 
impedance that is not equal to the characteristic impedance of 
the line. Sometimes this may be intentional but most often it is 
simply because the correct terminating impedance is not possi- 
ble, or is not available. In a radio system the terminating 
impedance is usually an aerial. This will have an impedance 
which depends upon the type of aerial and it is not always 
convenient to use a line having the same value of characteristic 

When the impedance terminating a line is not equal to the 

characteristic impedance, the line is said to be incorrectly 

, terminated or mismatched. Since the line is not matched, the 


Fig. 4.2 Open-circuited loss-free 

load is not able to absorb all the power incident upon it and so 
some of the power is reflected back towards the sending end of 
the line. 

Consider Fig. 4.2 which shows a loss-free line whose output 
terminals are open circuited. The line has an electrical length 
of one wavelength and its input terminals are connected to 
a source of e.m.f. E s volts and impedance Z ohms. 

When the generator is first connected to the line, the input 
impedance of the line is equal to its characteristic impedance 
Z . An incident current of EJ2Z then flows into the line and 
an incident voltage of EJ2 appears across the input terminals. 
These are, of course, the same values of sending-end current 
and voltage that flow into a correctly-terminated line. The 
incident current and voltage waves propagate along the line, 
being phase-shifted as they travel. Since the electrical length of 
the line is one wavelength, the overall phase shift experienced 
is 360°. 

Since the output terminals of the line are open-circuited, no 
current can flow between them. This means that all of the 
incident current must be reflected at the open-circuit. The total 
current at the open-circuit is the phasor sum of the incident 
and reflected currents, and since this must be zero the current 
must be reflected with 180° phase shift. The incident voltage is 
also totally reflected at the open circuit but with zero phase 
shift. The total voltage across the open-circuited terminals is 
twice the voltage that would exist if the line were correctly 
terminated. The reflected current and voltage waves propagate 
along the line towards its sending-end, being phase-shifted as 
they go. When the reflected waves reach the sending end, they 
are completely absorbed by the impedance of the matched 

At any point along the line, the total current and voltage is 
the phasor sum of the incident and reflected currents and 
voltages. Consider Fig. 4.3. At the open-circuit the phasors 
representing the incident and reflected currents are of equal 
length (since all the incident current is reflected) and point in 
opposite directions. The current flowing in the open circuit is 
the sum of these two phasors and is therefore zero as ex- 
pected. At a distance of A/8 from the open circuit, the incident 
current phasor is 45° leading, and the reflected current phasor 
is 45° lagging on the open-circuit phasors. The lengths of the 
two phasors are equal since the line loss is zero but they are 
90° out of phase with one another. The total current at this 
point is \l2 times the incident current. Moving a further A/8 
along the line, the incident and reflected current phasors have 
rotated, in opposite directions, through another 45° and are 
now in phase with one another. The total current A/4 from the 
open circuit is equal to twice the incident current. A further 













Fig. 4.3 (a) The incident current, (b) 
the reflected current at A/8 intervals 
along a loss-free open-circuited line, 
(c) the r.m.s. value of the total cur- 
rent at each point 

Distance from open circuit 

A/8 along the line finds the two phasors once again at right 
angles to one another so that the total line current is again V2 
incident current. At a point A/2 from the end of the line, the 
incident and reflected current phasors are in antiphase with 
one another and the total line current is zero. Over the next 
half-wavelength of line the phasors continue to rotate in 
opposite directions, by 45° in each A/8 distance, and the total 
line current is again determined by their phasor sum. 

It is usual to consider the r.m.s. values of the total line 
current and then its phase need not be considered. The way in 
which the r.m.s. line current varies with distance from the 
open-circuit is shown by Fig. 4.3 c. The points at which maxima 
(antinodes) and minima (nodes) of current occur are always 
the same and do not vary with time. Because of this the 
waveform of Fig. 4.3c is said to be a STANDING WAVE. 

If, now, the voltages existing on the line of Fig. 4.2 are 
considered, the phasors shown in Fig. 4.4 are obtained. At the 
open-circuited output terminals, the incident and reflected 
voltage phasors are in phase and the total voltage is twice the 
incident voltage. Moving from the open circuit towards the 
sending end of the line, the phasors rotate through an angle of 
45° in each A/8 length of line; the incident voltage phasors 
rotate in the anti-clockwise direction and the reflected voltage 
phasors rotate clockwise. The total voltage at any point along 
the line is the phasor sum of the incident and reflected voltages 
and its r.m.s. value varies in the manner shown in Fig. 4.4c. 

Two things should be noted from Figs. 4.3c and Fig. 4.4c. 
Firstly, the voltage standing-wave pattern is displaced by A/4 


"-M/- M 












Fig. 4.4 (a) The incident voltage, (b) 
the reflected voltage at A/8 intervals 
along a loss-free open-circuited line, 
(c) the r.m.s. value of the total vol- 
tage at each point 

■ Incident 

Distance from open circuit 


from the current standing-wave pattern, i.e. a current antinode 
occurs at the same point as a voltage node and vice versa. 
Secondly, the current and voltage values at the open circuit are 
repeated at A/2 intervals along the length of the line; this 
remains true for any longer length of loss-free line. 

When the output terminals of a loss-free line are short cir- 
cuited, the conditions at the termination are reversed. There 
can be no voltage across the output terminals but the current 
flowing is twice the current that would flow in a matched load. 
This means that at the short circuit the incident current is 
totally reflected with zero phase shift and the incident voltage 
is totally reflected with 180° phase shift. Thus, Fig. 4.3c shows 
how the r.m.s. voltage on a short-circuited line varies with 
distance from the load, and Fig. 4.4c shows how the r.m.s. 
current varies. 

Clearly, neither an open-circuited nor a short-circuited line 
can be used for the transmission of information from one point 
to another. Either condition might arise because of a fault but 
might be intended, particularly the short-circuit, when the line 
is to be used to simulate an electrical component. 

Open and short-circuit terminations are the two extreme 
cases of a mismatched line and in most cases the mismatched 
load will have an impedance somewhere in between. The 
fraction of the incident current or voltage that is reflected by 
the load is determined by the REFLECTION COEFFICIENT 
of the load. The voltage reflection coefficient p v is the ratio 
reflected-voltage/incident-voltage, and the current reflection 
coefficient p t is the ratio reflected-current/incident-current, at 
the load. Always p t = —p v . 



The incident current at the output terminals of a mismatched line is 
5 mA. If the current reflection coefficient of the load is 0.5, what is 
the reflected current? 


Reflected current = 0.5 x 5 = 2.5 mA (Arts.) 

The voltage reflection coefficient is determined by the values 
of the characteristic impedance of the line and the load impe- 
dance. Thus, 

Pv =^—^ (4.11) 

The magnitude of the voltage reflection coefficient lies in the 
range ±1, the limits corresponding to the cases of open and 
short-circuited loads. 


Calculate the voltage reflection coefficient of a line of 50 CI 
characteristic impedance terminated by an impedance of (i) 50' fl, (ii) 
30 ft, (iii) 100 ft 


(i) From equation (4.11) 

50-50 „ /A s 

ft= 50+lu =0 (Am - ) 

This answer is to be expected since, if the line is matched, Z = Z L 
and there is no reflection. 

30-50 / 

(ii) ft =^7^ = -0.25 = 0.25480! (Ana.) 

100-50 / 

(iii) ft = 100 + 50 = °- 33 = 0-33^ (Ans.) 

When the reflection coefficient is less than unity, the 
reflected current and voltage at any point along a loss-free line 
will be smaller than the incident values. Then the maximum 
current or voltage on the line will be less then twice the 
incident current and voltage, and the minimum current or 
voltage will not be zero. Suppose, for example, that p v = 0.5 
A)° . Then the maximum line voltage will be 1.5 times the 
incident voltage and will occur at the load and at multiples of 
A/2 from the load. The minimum line voltage will be 0.5 times 
the incident voltage and will occur A/4 from the load and then 
at multiples of A/2 from that point. Similarly, the maximum 
line current will be 1.5 times and the minimum line current 
will be 0.5 times the incident current. Maxima of voltage will 
occur at the same points as minima of current and vice versa. 
Fig. 4.5 shows the standing waves of current and voltage on a 
loss-free line with a load voltage reflection coefficient of 0.5^!. 


Fig. 4.5 Standing wave pattern on 
a mismatched line with p^ = 0-5/0° 

Voltage s 










X X 





2 4 
Distance from load 

0.5 V,-, 0.5/,- 

Standing Wave Ratio 

An important parameter of any mismatched low-loss transmis- 
sion line is its VOLTAGE STANDING-WAVE RATIO or 
v.s.w.r. The v.s.w.r. is the ratio of the maximum voltage on the 
line to the minimum voltage, i.e. 

S=V nm JV mbl (4.12) 

The maximum voltage on a mismatched line occurs at those 
points where the incident and the reflected voltages are in 
phase with one another. Also, the minimum line voltage exists 
at those points along the line at which the incident and 
reflected voltages are in antiphase. Therefore 

v,+|a,|v, 1+Ia.I 

Vi-lft.IV, l-kl 
where V { is the incident voltage. 



A low-loss line whose characteristic impedance is 70 fi is terminated 
by an aerial of 75 £1 impedance. Determine the v.s.w.r. on the line. 


From equation (4.11) 

75-70 , 

p„= = 0.035 fc 

** 75+70 L - 

Therefore, from equation (4.12) 





The presence of a standing wave on an aerial feeder is 
undesirable for several reasons and very often measures, 
beyond the scope of this book, are taken to approach the 
matched condition and to minimize reflections. The reasons 
why standing waves on a feeder should be avoided if at all 
possible are as follows: 


(a) Maximum power is transferred from a transmission line 
to its load when the load impedance is equal to the 
characteristic impedance. When a load mismatch exists, 
some of the incident power is reflected at the load and 
the transfer efficiency is reduced. 

(b) The power reflected by a mismatched load will propa- 
gate, in the form of current and voltage waves, along the 
line towards its sending end. The waves will be at- 
tenuated as they travel and so the total line loss is 

(c) At a voltage maximum the line voltage may be anything 
up to twice as great as the incident voltage. For low- 
power feeders, such as those used in conjunction with 
radio receivers, the increased voltage will not matter. 
For a feeder connecting a high power radio transmitter 
to an aerial, however, the situation is quite different. 
Care must be taken to ensure that the maximum line 
voltage will not approach the breakdown voltage of the 
line's insulation. This means that for any given value of 
v.s.w.r. there is a corresponding peak value for the 
incident voltage and hence for the maximum power that 
the feeder is able to transmit. A high v.s.w.r. on a feeder 
can result in dangerously high voltages appearing at the 
voltage antinodes. Great care must then be taken by 
maintenance staff who are required to work on, or near 
to, the feeder system. 

Measurement of V.S.W.R. 

The v.s.w.r. on a mismatched transmission line can be deter- 
mined by measuring the maximum and minimum voltages that 
are present on the line. In practice, the measurement is 
generally carried out using an instrument known as a 
STANDING- WAVE INDICATOR. Measurement of v.s.w.r. 
not only shows up the presence of reflections on a line but it 
also offers a most convenient method of determining the 
nature of the load impedance. 

The measurement procedure is as follows. The v.s.w.r. is 
measured and the distance in wavelengths from the load to the 
voltage minimum nearest to it is determined. The values 
obtained allow the magnitude and angle of the voltage reflec- 
tion coefficient to be calculated. Then, using equation (4.11), 
the unknown load impedance can be worked out. Unfortu- 
nately the arithmetic involved in the latter calculation is fairly 
lengthy and tedious, and it is customary to use a graphical aid 
known as the Smith chart which simplifies the work. 

If the load impedance is purely resistive, a much easier 
method of measurement is available. Suppose, for example, 


that Z L = R L = 3R . (Remember that Z is always purely 
resistive at radio frequencies.) Then, 

_ Zj_ — Z _ 3Rp— Rq _ 1 frw 

Z L + Z 3R +R 

1+kL i+j 
l-kl i-l 

Now suppose that instead Z L = R L = ^R . Then 

r /180° 

3^0 + ^O 


S = - — j = 3 as before 

It should be noted that the v.s.w.r. is equal to the ratio 
RJZ or Z IR L . This simple relationship is always true pro- 
vided the line losses are negligibly small and the load impe- 
dance is purely resistive. 


The v.s.w.r. on a loss-free line of 50 £2 characteristic impedance is 
4.2. Determine the value of the purely resistive load impedance which 
is known to be larger than 50 il. 


RJZo = S = 4.2 

i? L = SZ = 4.2 x 50 = 210 n (Ans.) 

Radio Station Feeders 

A feeder is employed to connect an aerial to the radio trans- 
mitter or receiver with which it is associated. Feeders are 
usually either two-wire or twin conductors, about 0.3 m apart 
mounted on top of wooden poles, or are coaxial pairs. The 
twin feeders are normally operated balanced with respect to 
earth, but the coaxial feeders have their outer conductor 
earthed and are therefore unbalanced. The two types of feeder 
have various advantages and disadvantages relative to one 
another and these are listed below. 


(a) Twin feeders are cheaper to provide than coaxial pairs. 

(b) It is easier to carry out v.s.w.r. measurements and locate 
faults on a twin feeder. 

(c) Matching devices are commonly used in feeder systems 
to convert a mismatched aerial load into a more or less 
matched load. These matching devices are easier and so 
cheaper to make when manufactured for use in a twin 
feeder system. 

(d) Coaxial feeder is less demanding in its use of space than 
is twin feeder. 

(e) Both the conductors comprising a twin feeder are ex- 
posed to the atmosphere and this leads to the two-wire 
feeder's transmission characteristics being much more 
variable than those of a coaxial feeder. 

(/) At higher frequencies the two conductors of a twin 
feeder are electrically spaced well apart and tend to 
radiate energy. Because of this the two-wire feeder has 
greater losses. 

(g) In many radio stations it is often necessary to switch 
feeders between aerials and between station equipment 
as propagation conditions vary. The necessary switching 
arrangements are much easier to augment in conjunction 
with coaxial feeder than with twin feeder. 

Most high-frequency transmitting stations use a combination 
of the two types of feeder in an attempt to make use of the 
advantages of each type. Within the radio station building 
coaxial feeders are used but to connect the building to the 
aerials the twin feeder is employed. 


4.1. (a) Why is it necessary to match an aerial to its feeder? (b) 
What do you understand by the terms (i) reflection coefficient 
and (ii) voltage standing wave ratio as used with reference to an 
aerial and feeder system, and what is the relationship between 
them? (part C&G) 

4.2. (a) Why is it necessary to match an aerial to its feeder? (b) 
What do you understand by the term voltage standing wave 
ratio? (c) Given a choice between typical balanced and unbal- 
anced feeder systems, which would you choose (i) on a cost 
basis, (ii) for a high-power handling application, (iii) for a very 
high frequency application, (iv) to connect a transmitter to a 
rhombic aerial, (v) to connect a receiver to a Yagi aerial? 

(part C&G) 

4.3. Describe the circumstances in which a standing wave can arise 
on a transmission line and state the meaning of standing wave 
ratio. An h.f. transmission line of negligible loss has a charac- 
teristic impedance of 600 ft and is terminated by an aerial. 
Calculate the standing wave ratio along the line when the aerial 
impedance is 500 ft. (part C&G) 


4.4. A radio-frequency transmission line has a characteristic impe- 
dance of 75 ft and a phase velocity of propagation of 2.4 x 
10 8 m/s. Determine its inductance and capacitance per metre. 

4.5. (a) What is meant by the following terms when applied to a 
radio-frequency transmission line: (i) voltage reflection coeffi- 
cient, (ii) voltage standing wave ratio, (iii) wavelength? (b) The 
v.s.w.r. on a line is 1.05. Calculate its voltage reflection coeffi- 

4.6. Describe, in your own words, how a line discontinuity or 
mismatch will produce standing waves of current and voltage. 

4.7. Using the expression for the voltage reflection coefficient of a 
mismatched transmission line explain why there are no reflec- 
tions on a correctly terminated line. List the reasons why the 
presence of a standing wave on an aerial feeder is undesirable. 

4.8. A correctly-terminated line is 2000 m in length and has a 
characteristic impedance of 600 ft. (a) What is the impedance 
(i) at the load, (ii) 1000 m from the load, (iii) 1500 m from the 
load? (fc) Explain why the current 100 m from the sending end 
of the line will lag the sending-end current, (c) The line has an 
attenuation coefficient of 2dB/km at a particular frequency. 
What is its overall loss at twice this frequency? 

Short Exercises 

4.9. A transmission line is 20 metres long. Is it an electrically short 
or long line? Give reasons for your answer. 

4.10. What is meant by the term characteristic impedance when 
applied to a radio-frequency transmission line? A line has a 
characteristic impedance of 60 ft and its output terminals are 
connected to the input terminals of a 100 m length of another 
line. The second line has a characteristic impedance of 60 ft 
and is correctly terminated. Determine the input impedance of 
the first line. 

4.11. The v.s.w.r. on a loss-free r.f. line is 5. If the minimum voltage 
on the line is 1 volt what is the maximum voltage? 

4.12. An r.f. line has v.s.w.r. of 2.2. Calculate the magnitude of its 
current reflection coefficient. 

4.13. List the reasons why a high standing wave ratio is undesirable 
on an aerial feeder. 

4.14. What are the minimum and maximum value of v.s.w.r. that can 
exist on a transmission line? What load impedances do they 
correspond to? 




In a radio communication system, the baseband signal is 
positioned in a particular part of the frequency spectrum using 
some form of modulation. The modulated wave is then 
radiated into the atmosphere, in the form of an electromagne- 
tic wave, by a transmitting aerial. For the signal to be received 
at a distant point, the electromagnetic wave must be inter- 
cepted by a receiving aerial. The basic principles of aerials, and 
the meanings of various terms used with them, have been 
discussed in a previous volume [RSII] and a knowledge ~of 
these will be assumed in this chapter. A large number of 
different kinds of aerial are in existence but only four of them 
are commonly used in modern radio-telephony systems. These 
four aerials, namely the Yagi, the rhombic, the log-periodic, 
and the parabolic reflector, will each be described. 

The characteristics of any aerial, such as its efficiency and its 
radiation pattern are the same whether the aerial is used for 
transmission or reception, but in this chapter the description 
will be in terms of transmission. The main differences between 
practical transmitting and receiving aerials are the (often) 
tremendously different powers which have to be handled. For 
example, a transmitting aerial may radiate many kilowatts of 
power while a receiving aerial may have only a few milliwatts 
dissipated in it. Other than this, the main requirement of a 
transmitting aerial is that it should match its feeder in order to 
ensure maximum power input to the aerial. For a receiving 
aerial, the priority is for maximum gain and directivity and for 
minimum sidelobes. 




Fig. 5.1 The A/2 dipole 

The Yagi Aerial 

The Yagi aerial is made up of a A/2 dipole and a number of 
parasitic elements. A A/2 dipole is a conductor whose electrical 
length is one-half the wavelength at the desired frequency of 
operation, and which is centre fed (see Fig. 5.1). The current 
and voltage distributions in a A/2 dipole can be deduced from 
the current and voltage distributions of a A/4 length of low-loss 
open-circuited transmission line. 

Refer back to Fig. 4.3 which shows the current and voltage 
standing waves on a A loss-free line. Over the first A/4 distance 
from the open-circuit, the current rises from zero to a max- 
imum, and the voltage falls from a maximum to zero, with the 
waveforms shown in Fig. 5.2. Similar standing-wave patterns 


Distance from open circuit 

Fig. 5.2 Current and voltage dis- 
tributions on an open-circuited A/4 
loss-free line 



Fig. 5.3 Current and voltage dis- 
tributions on a A/2 dipole showing 
(a) r.m.s. values and (fa) peak values 

will be obtained if the two conductors forming the line are 
opened out through an angle of 90° to form a A/2 dipole aerial. 
Fig. 5.3a shows the r.m.s. current and voltage distributions on 
a A/2 dipole, while Fig. 5.3b shows the distributions when 
peak values are considered. However, once the conductors are 
opened out and their separation increased, they will radiate 
energy. The resultant line losses modify the standing-wave 
pattern slightly so that the voltage no longer falls to zero at the 
centre of the dipole. 

Impedance of a Dipole 

Impedance is the ratio of voltage to current and it is evident 
from Fig. 5.3a that this ratio is not a constant quantity. At the 


two ends of the dipole, the voltage is large and the current is 
small, so the impedance is high, typically about 3500 ft. At the 
centre of the dipole the current is large and the voltage is small 
(not zero because of losses), and the dipole impedance is 73 ft. 
This is also the value of the radiation resistance of the aerial. 
When the impedance of an aerial is referred to, it is necessary 
to specify the point on the aerial which is to be considered. 
Usually, as would be expected, the input terminals are chosen. 

The INPUT IMPEDANCE of a dipole aerial varies with 
frequency in the same way as the impedance of a series-tuned 
circuit. When the aerial is resonant, its electrical length is A/2 
and its input impedance is purely resistive and equal to 73 ft. 
(The physical length is about 5% shorter than A/2.) At fre- 
quencies higher than the resonant frequency, the signal 
wavelength is reduced and the dipole becomes electrically 
longer than A/2. Its input impedance is now inductive. When 
the frequency is reduced below its resonant value, the electri- 
cal length of the dipole becomes less than A/2 and its input 
impedance is capacitive. The current fed into the aerial will 
have its maximum value when the aerial is of resonant length 
and, since the radiated power is proportional to the square of 
the current, the aerial is then at its most efficient. 

The reactive component of the input impedance of the 
dipole is a function of the diameter of the conductor. The 
thicker the conductor the smaller the change in input reac- 
tance for a given change in frequency. Thus, when a wide 
bandwidth is required, a thick conductor must be employed. 

Fig. 5.4 Radiation patterns of a ver- 
tical A/2 dipole: (a) horizontal plane 
pattern, (to) vertical plane pattern 

/Equal radiation 
in all directions 

Vertical dipole 

No radiation in 
direction of 
aerial axis 



The radiation pattern in the horizontal plane of a vertical 
A/2 dipole is a circle as shown in Fig. 5.4a. The RADIATION 
PATTERN is a graphical representation of the way in which 
the electric field strength produced by an aerial varies at a 
fixed distance from the aerial, in all directions in that plane. 
Hence, the circular radiation pattern means that the dipole will 
radiate energy equally well in all directions in the horizontal 


Fig. 5.5 A/2 dipole with (a) a reflec- 
tor and (b) a director 

plane. In the vertical plane, the vertical A/2 dipole does not 
radiate energy equally well in all directions. Indeed, in some 
directions it does not radiate at all as shown by the radiation 
pattern of Fig. 5.46. For many radiocommunication systems, 
other than (most) sound or television broadcasting services, 
the radiated energy should be concentrated in one or more 
particular directions, and so some degree of DIRECTIVITY is 

An increase in the directivity of a A/2 dipole can be obtained 
by the addition of a parasitic element known as a REFLEC- 
TOR. A reflector is a conducting rod, approximately 5% 
longer than A/2, mounted on the side of the aerial remote from 
the direction in which maximum radiation should be directed 
(Fig. 5.5a). The reflector is said to be a PARASITIC ELE- 
MENT because it is not electrically connected to the dipole or 





nni Jn$ 


Direction of 





Fig. 5.6 Radiation patterns: (a) A/2 
dipole and reflector: in equatorial 
plane, (b) A/2 dipole and reflector: in 
meridian plane, (c) A/2 dipole, reflec- 
tor and director: in equatorial plane 







Direction of transmission 



to the feeder. The reflector will affect the radiation pattern of 
the A/2 dipole because e.m.f.s are induced into it and cause it 
to radiate energy. The exact effect produced depends upon the 
length of the reflector and its distance from the dipole. Fig. 
5.6a,b illustrates one possibility; clearly the directivity of the 
array is better than that of the dipole on its own. 


The action of the reflector effects this improvement as 
follows. When a voltage, at the resonant frequency of the 
dipole, is applied to the aerial, an in-phase current flows and 
the dipole radiates an electromagnetic wave that is in phase 
with the current. This energy is radiated equally well in all 
directions perpendicular to the dipole. Some of this energy will 
arrive at the reflector and induce an e.m.f. in it that will lag 
the voltage applied to the dipole by an angle determined by 
the element spacing. If, for example, the spacing is 0.15 A, the 
induced e.m.f. lags the dipole voltage by 180°. The induced 
e.m.f. will cause a lagging current to flow in the reflector. The 
reflector will now also radiate energy in all directions normal 
to it. If both the length of the reflector and the dipole/reflector 
spacing have been chosen correctly, the energy radiated by the 
reflector will add to the energy radiated by the dipole in the 
wanted direction. Conversely in the opposite direction, i.e. 
dipole to reflector, the dipole and reflector radiations will 
subtract from one another. 

Further increase in the directivity and gain of a dipole aerial 
can be achieved by the addition of another parasitic element 
on the other side of the dipole. This element, known as a 
DIRECTOR, is made about 5% shorter than the A/2 dipole. 
When the dipole radiates energy, an e.m.f. is induced into the 
director (as well as the reflector) and a leading current flows in 
it. The director then radiates energy in all directions normal to 
it. The length of the director and its distance from the dipole 
are both carefully chosen to ensure that the field produced by 
the dipole is aided in the wanted direction and is opposed in 
the opposite unwanted direction. The effect of the director on 
the radiation pattern of the dipole/reflector array can be seen 
in Fig. 5.6c. 

A further increase in the gain and directivity of the aerial 
cannot be obtained by using a second reflector because the 
magnetic field behind the reflector has been reduced to small 
value. The addition of further directors will give extra gain, 
although the increase per director falls as the number of 
directors is increased. This is shown by the graph given in Fig. 

In practice, the choice of element spacing must be a com- 
promise dictated by the gain and front-to-back ratio require- 
ments of the array. Usually, the dipole/reflector spacing is 
between 0.15 A to 0.25 A while the common dipole/director 
spacing is selected as a value somewhere in the range 0.1 A to 
0.15 A. 


An aerial array consists of a vertical A/2 dipole with a reflector and 





Fig. 5.7 Showing the relationship 
between the gain of a Yagi aerial 
and the number of directors 

16 18 20 

Number of directors 

one director. Calculate approximate dimensions and spacings for the 
elements if operation is to be at 100 MHz. 

A=3xl0 8 /100xl0 6 = 3m 


At 100 MHz 


A/2 = 1.5 m 

In practice, the dipole would be made slightly shorter because the 
electric field fringes out at each end of the dipole making its electrical 
length effectively longer. Therefore, 

Dipole length = 1 .48 m (Ans.) 

The reflector should be about 5% longer than A/2 and should be, 
say, 0.15 A behind the dipole. Therefore, 

Reflector length = 1.57 m (Ans.) 

Reflector/dipole spacing = 0.6 m (Ans.) 
The director should be about 5% shorter than A/2. Therefore, 

Director length = 1.43 m (Ans.) 

Director/dipole spacing = 0.4 m (Ans.) 

Folded Dipole 

The input impedance of a resonant A/2 dipole is 73 ft resistive. 
The addition of one or more parasitic elements reduces the 
input impedance to, perhaps, 50 ft with just a reflector and 
single director assembly, or perhaps only 20 ft if several 
directors are fitted. Normally a 50 ft or 75 ft coaxial feeder is 
used with a Yagi array, and so an impedance mismatch may 
exist at the aerial terminals which, as shown in Chapter 4, will 
produce a standing wave pattern on the feeder. 



Fig. 5.8 The folded \/2 dipole 

The difficulty could be overcome if the input impedance of 
the dipole could be increased in some way to a higher value. 
Then, the reduction in input impedance caused by the addition 
of parasitic elements would result in an impedance somewhere 
in the region of the 50 il or 75 CI characteristic impedance of 
the cable. The higher dipole impedance needed is easily ob- 
tained by using a folded dipole (see Fig. 5.8.). The input 
impedance of the folded dipole is four times larger than that of 
the straight dipole, i.e. it is equal to 4 x 73 = 292 O. Impedance 
multiplying factors other than four are possible by making the 
two halves of the folded dipole from different-diameter rods. 
The bandwidth of the Yagi array is also increased by the use of 
a folded dipole. A typical Yagi array is shown in Fig. 5.9. 

Since the current operation of a Yagi aerial depends criti- 
cally upon the lengths and spacings of the elements in terms of 
the signal wavelength, the aerial is only employed at v.h.f. and 
u.h.f. The physical dimensions necessary to operate in the h.f. 
band, or even more so in the medium waveband, would make 
the mechanical structure inconveniently large and correspond- 
ingly expensive. The bandwidth of the aerial is the range of 
frequencies over which the main lobe of its radiation pattern is 
within specified limits, generally —3 dB, and is of the order of 



Fig. 5.9 A practical Yagi aerial 



Coaxial feeder 

Yagi aerials are commonly used for the reception of televi- 
sion broadcast signals in the home and are visible on many 
rooftops. The aerial also finds considerable application in v.h.f. 
point-to-point radio-telephony systems for both transmission 
and reception. 

Typical performance figures for Yagi aerials are given in 
Table 5.1. 


Table 5.1 


Input impedance 




dB relative 
to A/2 dipole 












I 1SI 


Fig. 5.10 A long-wire radiator 

The Rhombic Aerial 

Point-to-point radio links operating in the h.f. band (3- 
30 MHz) are allocated three to five different frequencies to 
ensure a satisfactory service as sky-wave propagation condi- 
tions vary. The h.f. radio transmitters must be capable of 
rapidly changing frequency as and when required, and it is 
desirable, for economic reasons, to use the same aerial as 
much as possible. This requirement rules out the use of a 
resonant aerial such as the Yagi. A wideband aerial which is 
used for many h.f. links is the rhombic aerial; the rhombic is a 
TRAVELLING WAVE TYPE of aerial since its operation 
depends upon r.f . currents propagating along the full length of 
the aerial, and the formation of standing waves is avoided. 

Fig. 5.10 shows a conductor that is several wavelengths long 
and which, together with the earth, forms a transmission line 
of characteristic impedance Z and negligible loss. At the 
sending-end of the line, a generator of e.m.f. E s and impe- 
dance Z ohms is connected, and at the far end a terminating 
impedance of Z ohms is used. The input impedance of the 
line is Z and an input current I = EJ2Z flows and propagates 
along the line towards the far end. Since the line is correctly 
terminated, there are no reflections at the load and therefore 
no standing waves on the line. The line length / metres can be 
considered to consist of the tandem connection of a very large 
number of extremely small lengths 81 of line. Since the line 
losses are negligible, the current flowing in the line has the 
same amplitude at all points. This means that each elemental 
81 of line carries the same current I and is said to form a 

Each current element will radiate energy. The radiation 
from each element has its maximum value in the direction 
making an angle of 90° to the conductor and is zero along the 
axis of the conductor. The total field strength produced by the 
line at any point around it is the phasor sum of the field 
strengths produced by all of the current elements. The phase 
of the line current varies along the length of the line and in 
half -wavelength distances a 180° phase shift occurs. Because 


Fig. 5.11 



pattern of a 


Fig. 5.12 The rhombic aerial 

of this the field strengths produced by the current elements 
cancel out in the direction normal to the conductor to produce 
a null in the radiation pattern. Also, since no element radiates 
along the axis of the conductor, another null exists in this 
direction. Thus, the radiation pattern of an electrically long 
wire is as shown in Fig. 5.11 (a number of small lobes are also 
present but are not shown). The angle the two main lobes 
make with the conductor axis is dependent upon the electrical 
length of the conductor, decreasing as the conductor length is 
increased. When the length is between 4 A and 8 A, the 
relationship between lobe angle and frequency is a linear one 
between limits of 24° and 17°. 

The rhombic aerial consists of four such long wires con- 
nected together to form, in the horizontal plane, the geometric 
shape of a rhombus (Fig. 5.12). All the four wires will radiate 
energy in the directions indicated by its radiation pattern. The 
aerial is designed so that the main lobes of the radiation 
pattern of the wires are additive in the wanted direction and 
self-cancelling in the unwanted directions. This feature of the 
rhombic aerial is achieved by suitably choosing the angle 20 
subtended by two conductors. The TILT ANGLE (Fig. 
5.13) is chosen so that the lobe angle d is equal to (90-/3)°. 
Then the lobes marked X will point in opposite directions and 
the radiations they represent will cancel, and the lobes marked 
Y will point in the same (wanted) direction and their radiations 
will be additive. Since the lobe angle varies with frequency, 
it is not possible to choose the tilt angle to be correct at all the 
possible operating frequencies, and it is usual to design for 
optimum operation at the geometric mean of the required 
frequency band. 

Fig. 5.13 Illustrating the correct 
choice of tilt angle for a rhombic 


A rhombic aerial is to operate over the frequency band 7-14 MHz. 
Determine a suitable value for the tilt angle. 


The physical lengths of the four wires will be such that at 7 MHz they 
are 4 A and at 14 MHz they are 8 A long. Then at 7 MHz the lobe 
angle is 24° and at 14 MHz it is 17°. Since there is a linear relation- 
ship between the lobe angle and the frequency of operation, at the 
geometric mean of 7 MHz and 14 MHz, i.e. at 9.9 MHz, the lobe 
angle is approximately 20°. Therefore, 

Tilt angle = 90° - 0° = 90° - 20° = 70° (Ans.) 

At the design frequency the horizontal plane RADIATION 
PATTERN of a rhombic aerial is as shown in Fig. 5.14 with 
the radiated electromagnetic wave being horizontally polar- 
ized. The parts of the unwanted lobes that do not cancel are 
responsible for the sidelobes shown. At frequencies within the 


Fig. 5.14 Radiation 
rhombic aerial 

pattern of a 

bandwidth of the aerial but not at the design frequency, the 
wanted lobes do not point in exactly the same direction, and 
the effect on the radiation pattern is to increase its beamwidth 
and lower its gain in the wanted direction. Typically, a rhom- 
bic aerial will operate over a 2 : 1 frequency ratio, e.g. 7- 
14 MHz with a gain, relative to a A/2 dipole, that varies with 
frequency in the manner indicated by Fig. 5.15. 

Since the rhombic aerial is primarily used with sky-wave 
propagation systems, the energy radiated by the aerial must be 
directed towards the ionosphere at the correct angle of eleva- 
tion. The ANGLE OF ELEVATION of the main lobe is 

S 20 

o 15 


Fig. 5.15 Gain/frequency charac- 
teristic of a rhombic aerial 






24 28 

Frequency (MHz) 


Fig. 5.16 Optimum height above 
ground for a rhombic aerial 

determined by the height at which «the four conductors are 
mounted above the earth. For the main lobe to be at the 
required angle of elevation, the energy radiated downwards 
towards the ground must be reflected at such an angle that it is 
then in phase with the directly-radiated energy (Fig. 5.16). 
The field strength produced in the wanted direction is then 
doubled, which corresponds to an increase in gain of 6 dB. 

The INPUT IMPEDANCE of a rhombic aerial is deter- 
mined by both the signal frequency and the diameter of the 
wires and is in the range 600 O to 800 CI. The input impe- 
dance is frequency-dependent and can be made more nearly 
constant by using more than one wire to form each arm of the 
rhombus. The input impedance is then also a function of the 
number of wires used and their distance apart. 

characteristic impedance of the lines forming the aerial in 
order to prevent reflections taking place and this means that 
one-half of the power fed into the aerial will be dissipated in 
the terminating impedance; the aerial, therefore, has a max- 
imum efficiency of 50%. When the powers involved are small, 
as with a receiving rhombic aerial, a carbon resistor will often 
suffice as the terminating impedance. For high-power installa- 


Fig. 5.17 A practical rhombic aerial 

tions, such a simple solution is not available and commonly the 
impedance consists of a two-wire line using iron conductors. 

A typical rhombic aerial is illustrated by Fig. 5.17. 

The rhombic aerial possesses two disadvantages which are 
tending to lead to its replacement by the log-periodic aerial. 
Firstly, its radiation pattern exhibits relatively large sidelobes. 
Sidelobes in a radiation pattern are undesirable since, in a 
transmitting aerial, they mean that power is radiated in un- 
wanted directions. The energy may interfere with other sys- 
tems but, in any case, represents a waste of power. In the case 
of a receiving aerial the unwanted sidelobes indicate a re- 
sponse to interference and noise arriving from unwanted direc- 
tions. The second disadvantage, made clear by the typical 
dimensions given in Fig. 5.17, is the large site area which must 
be provided to accommodate a rhombic aerial. 

The Log-Periodic Aerial 

The log-periodic aerial provides an alternative to the rhombic 
aerial in the h.f. band and is particularly good when the 
available site area is limited and/or an elevation angle in excess 
of about 40° is required. The aerial can operate over a wide 
frequency band and has very small side- and back-lobes. 



© Q 


Fig. 5.18 

A/4 apart 

Two A/2 dipoles spaced 

Fig. 5.18 shows two vertical A/2 dipoles A and B which are 
A/4 apart at a particular frequency. They form a TWO- 
DIPOLE ARRAY. The two dipoles are fed with currents of 
equal amplitude but the current fed into dipole A leads the 
input current of dipole B by 90°. In the horizontal plane each 
dipole will radiate energy equally well in all directions. In the 
direction A to B, the energy radiated by dipole A has to travel 
a distance of A/4 before it reaches dipole B and will experience 
a phase lag of 90°. The field strengths produced by dipoles A 
and B are therefore in phase with one another and add. In the 
reverse direction B to A, the energy radiated by dipole B has a 
distance of A/4 to travel before it reaches dipole A. It will, 
therefore, have a total phase of - 180° relative to the energy 
radiated by dipole A. In the direction B to A the field 
strengths produced by dipoles A and B cancel out and so there 
is no radiation in this direction. In all other directions the field 
strengths produced by the two dipoles have a phase angle, 
other than 0° or 180°, between them and the resultant field 
strength is given by their phasor sum. 

The RADIATION PATTERN of the two-dipole array is 
shown in Fig. 5.19. Greater directivity and gain can be 
achieved by the addition of a third dipole C, A/4 apart from 
dipole B. Dipole C is fed with a current of equal amplitude to, 
but lagging by 90°, the current into dipole B. Similarly, a 
fourth, a fifth, and more dipoles can be added to further 
increase the directivity of the aerial. Unfortunately, the opera- 
tion of an end-fire array depends critically on the spacings of 
its component dipoles, and this means that the aerial is only 
suitable for operation at a single frequency. 

The log-periodic aerial provides an end-fire radiation pat- 
tern over a wide frequency band. The aerial is manufactured in 
various forms and Fig. 5.20a shows an example of the log- 
periodic dipole array which is used at v.h.f. The lengths l u l 2 , 
Z 3 , etc. of the dipoles increase from left to right with the 
relationship l 2 /li = l3/l2 = hlh etc., the common ratio being 
known as the scale factor t of the aerial. The spacings d u d 2 , 
d 3 , etc. between adjacent dipoles also increase from left to 
right. Successive spacings are also related by the same scale 
factor t. 

The input signal is applied to the aerial via a twin feeder and 
is applied to adjacent dipoles with 180° phase change because 
the connections to successive dipoles are reversed. At any 
given frequency within the bandwidth of the aerial, only two, 
or, perhaps, three dipoles are at or anywhere near resonance, 
i.e. approximately A/2 long. These dipoles take a relatively 
large input current and radiate considerable energy; because 
of the phasing of the dipole currents, an end-fire effect is 


Fig. 5.19 Horizontal plane radiation 
pattern of two vertical A/2 dipoles 
spaced A./4 apart, fed with equal 
amplitude currents 

Fig. 5.20 (a) The log-periodic di- 
pole aerial: general principle 

Fig. 5.20 (b) Practical example of a 
log-periodic aerial 


< a ' (b) 

Fig. 5.21 Radiation pattern of a log- 
periodic dipole aerial 

obtained, with the main lobe being in the direction of from 
longer elements to shorter elements. All the other dipoles are 
now either much longer or much shorter than A/2 and radiate 
little or no energy. The radiation pattern of a log-periodic 
dipole aerial is shown in Fig. 5.21. The equatorial plane 
pattern is given in a and the meridian plane pattern in b. 

As the frequency of the input signal is varied, the ACTIVE 
REGION of the aerial will move in one direction or the other. 
If the frequency is reduced, the active region will move to- 
wards the end of the aerial where the dipoles are longer. If the 
frequency is increased, shorter dipoles become resonant or 
nearly resonant and the active region moves towards the short 
element end of the aerial. The dipole array can be mounted on 
top of a pole or mast and oriented to operate with either 
vertical or horizontal elements. Fig. 5.20b shows a typical 
example of a log-periodic dipole aerial. 

Supporting glass fibre/polyester rope 

Mounting post 

"Rope anchor 

Fig. 5.22 A high-frequency log- 
periodic aerial 

A HIGH-FREQUENCY VERSION of the log-periodic 
aerial is shown in Fig. 5.22. Since the aerial is mounted close 
to the earth, its vertical plane radiation pattern is modified by 
earth reflections. If it is desired to have the same elevation 
angle for the radiation pattern at all frequencies, each element 
must be at the same electrical height above the ground. This, 
of course, means that the physical height of the aerial above 
earth must vary along the length of the aerial as shown in the 

Log-periodic aerials are used for h.f. communication links 
where the wide bandwidth, 4-30 MHz, is often an advantage. 
The input impedance of the aerial lies in the range of 50-300 
ft and the gain is about 10 dB relative to a X./2 dipole, which 
can be increased to about 14 dB by earth reflections. 


The gain is less than that of the rhombic, which is an 
indication of a radiation pattern that is not very directive. On 
the other hand its side- and back-lobe levels are small. 

Compared to the Yagi aerial, the v.h.f. log-periodic aerial 
has a smaller gain (for the same number of elements), and 
smaller side- and back-lobes. 

The Parabolic Reflector Aerial 

At frequencies at the upper-end of the u.h.f. band and in the 
s.h.f. band, the signal wavelength becomes sufficiently small to 
allow a completely different kind of aerial to be used. The 
aerial is known as the parabolic reflector or DISH aerial and it 
is capable of producing a very directive, high-gain radiation 

Fig. 5.23 Reflection from a para- 
bolic reflector 

The aerial consists of a large metal dish which is used to 
reflect into the atmosphere the radio energy directed onto it by 
a smaller radiator (often a dipole/reflector array) mounted at 
the focal point. The idea of the aerial is illustrated by Fig. 
5.23. A property of a parabolic dish is that the distance from 
the focal point of the dish to an arbitrary plane the other side 
of the focal point is a constant regardless of which point on the 
dish is considered, i.e. 

-> RAX = RBX = RCX = RDX = REX = RFX 

Because of this property, the spherical wavefront signal 
originating from the radiator and reflected by the dish arrives 
at the plane X with a plane wavefront. The reflected waves are 


all parallel to one another and form a concentrated, highly- 
directive radio wave. 

When used as a receiving aerial, the action of the dish is 
reversed; the incoming plane wavefront radio wave is reflected 
by the dish and brought to a focus at the focal point where a 
small receiving aerial, such as a A/2 dipole, is mounted and is 
connected to the feeder. 

The GAIN of a parabolic dish aerial depends upon its 
diameter in terms of the signal wavelength. If the diameter is 
made several times larger than the signal wavelength, very 
high gains can be obtained. The relationship between aerial 
gain and the diameter D of the dish is given by equation (5.1): 

Gain = 6(D/A) 2 (5.1) 

The beamwidth of the aerial is also a function of the dish 

Beamwidth = 70 A/D (5.2) 


A parabolic dish aerial has a diameter of 1 m. Determine its gain at (i) 
1 GHz, (ii) 6 GHz. 


(i) Signal wavelength A = 3 x 10 8 /10 9 = 0.3 m 

Therefore, from equation (5.1) 





(ii) A=3xl0 8 /6xl0 9 = 0.05m 



= 2400 (Ans.) 


Fig. 5.24 Two views of a parabolic 
dish aerial 

Angular distance from direction of 
maximum radiation 

Fig. 5.25 Radiation pattern of a 
parabolic dish aerial 


Fig. 5.24 shows the appearance of a practical dish aerial. 

The radiation pattern of a parabolic reflector has one main, 
uery-narrow-beamwidth lobe and a number of much smaller 
sidelobes. The main lobe is so narrow that the radiation 
pattern cannot conveniently be plotted in the usual manner. 
Usually, the radiation pattern is only drawn for a small angular 
distance either side of the direction of maximum radiation, and 
Fig. 5.25 shows a typical pattern. 


5.1. From sketches of the radiation characteristics of a single non- 
resonant wire develop the radiation patterns showing the direc- 
tional characteristics of a rhombic aerial. How do these charac- 
teristics vary with frequency? Describe how a transmitting 
rhombic aerial is terminated and describe the constructional 
features which provide a good impedance match over the 
required frequency band. (C & G) 

5.2. Describe the construction and action of a paraboloid aerial and 
sketch a typical radiation pattern. How are the gain and beam- 
width of such an aerial related to its diameter and the frequency 
of transmission? Sketch the device used for launching the radio 
energy into the aerials. {Part C & G) 

5.3. Explain clearly what is meant by the gain of an aerial. Sketch 
and describe a rhombic aerial suitable for h.f. transmission. 
What are the main design features that determine its perfor- 
mance? State typical values for (a) the gain, (b) the frequency 
bandwidth, and (c) the angle of elevation of the main lobe. 


5.4. Sketch and give dimensions of a high-power wide-bandwidth 
transmitting aerial used for long distance point-to-point h.f. 
services. Describe the method of feeding the aerial. How does 
the gain of the aerial vary with frequency? (C & G) 

5.5. Sketch, and give approximate dimensions in terms of 
wavelength for, a v.h.f. yagi aerial comprising a folded dipole 
with a reflector and director. For such an aerial state clearly 
what is meant by the terms (a) gain, (b) beamwidth, (c) 
bandwidth. Explain the purpose of the folded dipole. 


5.6. (a) What do you understand by the gain of an aerial? (ft) Draw 
a dimensioned sketch of a typical yagi aerial, (c) Give typical 
values for such an aerial of (i) gain, (ii) frequency band of 
operation, (d) Why is the yagi not commonly used at m.f.? (e) 
Why is the aerial fed via a folded dipole? (C & G) 

5.7. (a) Draw a dimensioned sketch of a rhombic aerial, (b) Why 
are three wires often employed on each leg of a rhombic aerial? 
(c) Upon what factors does the impedance of a rhombic aerial 
depend? (d) Why is it desirable to be able to alter the height of 
a rhombic aerial? (e) What is the most noticeable difference 
between a rhombic aerial used for receiving and one used for 


5.8. (a) Draw a dimensioned sketch of a yagi aerial suitable for 
operation at 200 MHz and explain why a folded dipole is 
normally used, (b) Draw the horizontal and vertical radiation 
patterns of (i) a vertical dipole, (ii) a vertical dipole with one 
reflector, (c) Show how the gain of an aerial relative to a dipole 
can be obtained from its radiation pattern. (C & G) 

5.9. Complete the table of comparison, Table 5.2, for the yagi, 
rhombic and log-periodic aerials as applied to a typical aerial of 
each type. (C & G) 

Table 5.2 




Operating frequency 



Input impedance 


For what service is 
it commonly used? 

Is it a travelling- 
wave aerial? 

Fig. 5.26 

5.10. Fig. 5.26 shows the horizontal radiation pattern of an aerial. 
Determine the gain of this aerial relative to a vertical A/2 


5.11. Sketch the construction of log-periodic aerial suitable for use in 
the h.f. band. Give typical values of gain and input impedance 
and state whether your aerial produces a horizontally- or a 
vertically-polarized wave. 

5.12. Sketch the radiation pattern of a half-wave dipole in both the 
equatorial and meridian planes. Show the current and voltage 
distributions in the aerial. Draw the arrangement of a simple 
yagi aerial with one director and show how the radiation 
pattern differs from that of the dipole alone. Label your aerial 
sketch with dimensions suitable for use at a frequency of (a) 
45 MHz, (b) 490 MHz. 

5.13. When an aerial radiates a power of 1 kW, a field strength of 
lOmV/m is set up at a certain distant point. Another aerial 
located alongside the first needs only to radiate 250 W to 
produce the same field strength at the same point. If the first 
aerial has a gain of 20 dB relative to an isotropic radiator, 
determine the gain of the second aerial. 

5.14. Describe the way in which energy is radiated from a conductor 
carrying a high-frequency current. Hence explain why aerials 
for use at v.h.f. are more efficient than those used at medium 
frequencies. Quote typical figures for aerial efficiency. An aerial 
has a loss resistance of 3 fl and a radiation resistance of 1 O. If 
the current fed into the aerial is 10 A calculate the aerial 
efficiency, and the power radiated. 

5.15. Explain the meanings of the following terms used in aerial 

(a) polarization (b) gain (c) radiation pattern 

(d) beamwidth (e) isotropic radiation 

(/) front-to-back ratio (g) parasitic element 

Short Exercises 

5.16. Draw the radiation patterns of a horizontal A/2 dipole in (a) the 
vertical plane and (b) the horizontal plane. 

5.17. Sketch, with dimensions in metres, a A/2 dipole with a reflector 
and one director array suitable for operation at 100 MHz. 

5.18. A dipole is 1.2 m long. At what frequency is this dipole a 
half-wavelength long? 

5.19. Write down typical figures for the gain and the input impedance 
of (i) a yagi aerial, (ii) a rhombic aerial, (iii) a log-periodic 

5.20. What is meant by (i) the radiation pattern, (ii) the beamwidth, 
and (iii) the gain of an aerial? 

5.21. Explain why directivity in a receiving aerial is desirable. 

5.22. Draw a folded A/2 dipole and say why and when it is used. 

5.23. A parabolic reflector is to have a gain of 1000. Calculate the 
diameter required if operation is at (i) 3 GHz, (ii) 3 MHz. 
Comment on your answer. 

C The Propagation of 
** Radio Waves 


When a radio-frequency current flows into a transmitting 
aerial, a radio wave at the same frequency is radiated in a 
number of directions as predicted by the radiation pattern of 
the aerial. The radiated energy will reach the receiving aerial 
or, in the case of broadcast or mobile systems, receiving 
aerials, by one or more of five different modes, of propagation^ 
Four of these modes, the surface wave, the sky wja^jhe Spiace 
vyflu^and the use of a communication satellite, are illustrated 
by Fig. 6.1. 

The surface wave is supported at its lower edge by the 
surface of the earth and is able to follow the curvature of the 
earth as it travels. The sky wave is directed upwards from the 
earth into the upper atmosphere where, if certain conditions 
are satisfied, it will be returned to earth at the required 
locality. The space wave generally has two components, one of 
which travels in a very nearly straight line between the trans- 
mitting and receiving aerials, and the other which travels by 
means of a single reflection from the earth. The fourth method 
illustrated is a relatively modern technique that utilizes the 
ability of a communication satellite orbiting the earth to re- 
ceive a signal, amplify it, and then transmit it at a different 
frequency towards the earth. The fifth method of propagation 
which is not shown in Fig. 6.1 is known as scatter and is used 
only when, for one reason or another, one of the other 
methods is not available. 

The radio frequency spectrum has been subdivided into a 
number of frequency bands and these are given in Table 6.1. 




Fig. 6.1 Modes of propagation 

Sky wave 
Space wave 

Surface wave 

Table 6.1 

Frequency band 



10-30 kHz 

Very low 


30-300 kHz 



300-3000 kHz 



3-30 MHz 



30-300 MHz 

Very high 


300-3000 MHz 

Ultra high 


3-30 GHz 

Super high 


The surface wave is used for world-wide communications in 
the v.l.f. and l.f. bands and for broadcasting in the m.f. bands. 

The sky wave is used for h.f. communication systems, in- 
cluding long-distance radio-telephony and sound broadcasting. 

The space wave is used for sound and television broadcast- 
ing, for multi-channel telephony systems, and for various 
mobile systems operating in the v.h.f., and u.h.f. and s.h.f. 

Communication satellite systems are used to carry interna- 
tional multi-channel telephony systems and sometimes televi- 
sion signals. 

Lastly, scatter systems operate in the u.h.f . band to provide 
multi-channel telephony links. 

The Ionosphere 

Ultra-violet radiation from the sun entering the atmosphere of 
the earth supplies energy to the gas molecules of the atmos- 
phere. This energy is sufficient to produce ionization of the 
molecules, that is remove some electrons from their parent 
atoms. Each atom losing an electron in this way has a resultant 
positive charge and is said to be ionized. 


The IONIZATION thus produced is measured in terms of 
the number of free electrons per cubic metre and is dependent 
upon the intensity of the ultra-violet radiation. As the radia- 
tion travels towards the earth, energy is continually extracted 
from it and so its intensity is progressively reduced. 

The liberated electrons are free to wander at random in the 
atmosphere and in so doing may well come close enough to a 
positive ion to be attracted to it. When this happens, the free 
electron and the ion recombine to form a neutral atom. Thus a 
continuous process of ionization and recombination takes 

At high altitudes the atmosphere is rare and little ionization 
takes place. Nearer the earth the number of^asmolecules per 
cubic metre is much greater and large numbers of atoms are 
ionized; but the air is still sufficiently rare to keep the proba- 
bility of recombination at a low figure. Nearer still to the 
earth, the number of free electrons produced per cubic metre 
falls, because the intensity of the ultra-violet radiation has 
been greatly reduced during its passage through the upper 
atmosphere. Also, since the atmosphere is relatively dense the 
probability of recombination is fairly high. The densjtvjafjree 

electrons is therefore ^a]Hmmedjatelj„aJto^ 
the earth, jjsp-s n* h'g h g r altitudes, and then falls again at still 
greater heights... The earth is thus surroufidecT by a wide belt of 
ionized gases, known as the IONOSPHERE. 

In the ionosphere, LAYERS exist within which the free 
electron density is greater than at heights immediately above 
or below the layer. Four layers exist in the daytime (the D, E, 
Fj and F 2 layers) at the heights shown in Fig. 6.2. 

500 km 

Fig. 6.2 Layers in the ionosphere 



-F2 layer 

-F 1 layer 
-E layer 
-D layer 

Electron density 
(electrons/m 3 ) 


The heights of the ionospheric layers are not constant but 
vary both daily and seasonally as the intensity of the sun's 
radiation fluctuates. The electron density in the D-laye r is 
small when c ompared with^lh^^theFlav^rsr ^ATru^t^tim e' 
"whSTthe ultra-violet r^^tionjiea^ses^no^more free electron s 
are produced and the O^layer^dtsappears because of the high 


rate of recombination at the lower altitudes. The E-layer is at 
a height of about 100 km and so the rate of recombination 
is smaller. Because of this, the E-layer, although becoming 
weaker, does not normally disappear at night-time. In the 
daytime, the F x layer is at a more or less constant height of 
200-220 km above ground but the height of the F 2 layer varies 
considerably. Typical figures for the height of the F 2 layer are 
250-350 km in the winter and 300-500 km in the summer. 

The region of the earth's atmosphere between the surface of 
the earth and the lower edge of the ionosphere is known as the 
TROPOSPHERE. The behaviour of the ionosphere when a 
radio waveMspropagated through it depends^very much upon 
the frequency^of the wave. At low frequencie s the ionosphere 
acts as though it were a medium of high electrical conductivity 
and reflects v /ith little loss, any signals incident on its lower 
edge. It is possible for a v.l.f. or l.f. signal to propagate for 
considerable distances by means of reflections from both the 
lower edge of the ionosphere and the earth. This is shown by 
Fig. 6.3. The wave suffers little attenuation on each reflection 
and so the received field strength is inversely proportional to 
the distance travelled. 

Fig. 6.3 Multi-hop transmission of 
a low-frequency wave 


In the m.f. band the D-layer acts as a very lossy medium 
whose attenuation reaches its maximum value at a frequency 
of 1.4_MHz, often known as the gyro-frequency. Generally, 
m.f. signals suffer so much loss in the D-layer that little energy 
reaches the E or F layers. At night-tmiejhiowever, the D-layer 
has disappea red and an m.f. signal will be refract ed by the 
E-layer and~perHaps~aIso by the F-layer^siTand returned to 
earth. With further increase in frequency to the h.f . band, the 
ionospheric attenuation falls and the E and F layers provide 
refraction of the sky wave. At these frequencies the D-layer 
has little, if any, refractive effect but it does introduce some 

The amount of refraction of a radio wave that an ionos- 
pheric layer is able to provide is a function of the frequency of 
the wave, and at v.h.f . a nd above no useful reflection is 
obtained ( usually). This means that a v.h.f. or s.h.f. signal will 
normally~pass straight through the ionosphere. 


/Wavefront (tilted forward) 

-Forward component 
s Resultant 

Fig. 6.4 Wavefront of the surface 

The Ground or Surface Wave 

At v.l.f. and l.f. the transmitting aerial is electrically short but 
physically very large and must therefore be mounted vertically 
on the ground. The aerial will radiate energy in several direc- 
tions and produce both surface and space waves (sometimes 
the sky wave too). The combined surface and space wave is 
known as the GROUND WAVE. At these frequencies the 
signal wavelength is long and the aerial height is only a small 
fraction of a wavelength. The reflected component of the space 
wave experiences a 180° phase shift upon reflection, and since 
the difference, in wavelengths, between the lengths of the 
direct and reflected waves is very small, the two waves cancel 
out. Because of this, v.l.f and l.f propagation is predominantly 
by means of the surface wave. Very often the term ground 
wave is used to represent the surface wave. 

The surface or ground wave is one which leaves the trans- 
mitting aerial very nearly parallel to the ground. Vertically 
polarized waves must be used because horizontal polarization 
would result in the low resistance of the earth short-circuiting 
the electric component of the wave. The surface wave follows 
the curvature of the earth as it travels from the transmitter 
because it is diffracted.^ Further bending of the wave occurs 
because the magnetic component of the wave cuts the earth's 
surface as it travels and induces e.m.f.s in it. The induced 
e.m.f.s cause alternating currents to flow and dissipate power 
in the resistance of the earth. This power can only be supplied 
by the surface wave, and so a continuous flow of energy from 
the wave into the earth takes place. The signal wavefront, 
therefore, has two components of velocity, one in the forward 
direction and one downwards towards the earth. The resultant 
direction is the phasor sum of the forward and downward 
components, and this results in the wave being tilted forward, 
as shown in Fig. 6.4. The downward component is always 
normal to the earth and the forward component 90° advanced; 
hence the tilted wavefront follows the undulations of the 
ground (Fig. 6.5). 

Fig. 6.5 Propagation of surface 
wave over undulating terrain 


t Diffraction is a phenomenon which occurs with all wave motion. It 
causes a wave to bend round any obstacle it passes. For a surface 
wave, the earth itself is the obstacle. 


The transfer of energy from the wave to the ground at- 
tenuates the wave as it travels, and the field strength E d at a 
distance d kilometres from the transmitter is given by 

E * = K Y (61) 

where E l is the field strength 1 km from the transmitter and K 
is a factor representing the wave attenuation caused by the 
power dissipated in the ground. 

The attenuation factor K depends upon the frequency of the 
wave, and the conductivity and permittivity of the earth. The 
atten uation a t a given frequency is least for propagation over 
expanses of water and greatest for propagation over _dry___ 
ground, such as dese rt. For^ropagaBbn over ground of aver- 
ligeTdampness, with a radiated power of 1 kW, the distance 
giving a field strength of 1 mV/m varies approximately with 
frequency as shown in Table 6.2. 

Table 6.2 


Range (km) 

100 kHz 

1 MHz 

10 MHz 

100 MHz 


At mi, particularly at the higher end of the band, the height 
of the aerial is a much larger fraction of the signal wavelength. 
Now complete cancellation of the direct and reflected compo- 
nents of the space wave no longer occurs and the space wave 
partially contributes to the field strength over shorter dis- 

Refraction of an Electromagnetic Wave 

When an electromagnetic wave travelling in one medium 
passes into a different medium, its direction of travel will 
probably be altered. The wave is said to be refracted. The ratio 

sine of angle of incidence, <f> t 
sine of angle of refraction, <f> r 

is a constant for a given pair of media and is known as the 
REFRACTIVE INDEX for the media. If one of the two 
media is air the absolute refractive index of the other medium 
is obtained. 

If a wave passes from one medium to another medium that 
has a lower absolute refractive index, the wave is bent away 
from the normal (Fig. 6.6a). Conversely, if the wave travels 


Medium 2 

^Pr S 

Medium 1 / 
/ 9/ 

(a) M2<f'\ 

Medium 2 
M 2 

(b) P 2 >Ml 

Fig. 6.6 Refraction of electro- 
magnetic waves: wave passing 
into a medium of (a) lower absolute 
refractive index; (fa) higher absolute 
refractive index 

into a region of higher absolute refractive index, the wave is 
bent towards the normal (Fig. 6.6ft). 

Suppose a wave is transmitted through a number of thin 
parallel strips (Fig. 6.7), each strip having an absolute refrac- 
tive index lower than that of the strip immediately below it. 
The wave will pass from higher to lower absolute refractive 
index each time it crosses the boundary between two strips, 
and it is therefore progressively bent away from the normal. If 
the widths of the strips are made extremely small, the absolute 
refractive index will steadily decrease and the wave will be 
continuously refracted. 

Within an ionospheric layer the electron density increases 
with increase in height above the earth. Above the top of the 
layer, the density falls with further increase in height until the 
lower edge of the next, higher layer is reached. At heights 
greater than the top of the F 2 -layer, the electron density falls 
until it becomes negligibly small. 

The refractive index n of a layer is related to both the 
frequency of the wave and the electron density according to 
equation (6.2): 

sin<fc // 81N\ 


Here / is the frequency of the radio wave in hertz, N is the 
number of free electrons per cubic metre, and as before 4>i and 
<f> r are respectively the angles of incidence and refraction. 

Fig. 6.7 Refraction of an elec- 
tromagnetic wave passing through 
media of progressively lower abso- 
lute refractive index: 

i "? 

j_^>»""" ! ^6 

j^^H ^ 5 

\ytr\ M 4 

b*Ci M3 

\j/\ \ ^2 

Strips of 






x Path of wave through strips 

Equation (6.2) shows that the refractive index of a layer 
decreases as the electron density is increased. This means that 
within a layer the refractive index falls with increase in height 
above ground. Also tcf be' noted is that an increase infre^. 
quency results in an increase in the refractive index of aTayer. 

A radio wave at a particular frequency ehteHng aTayeTwith 
angle of incidence <t> t will always be passing from lower to 
higher refractive index as it travels upwards through the layer. 
Therefore, the wave is continuously refracted away from the 
normal. If, before it reaches the top of the layer, the wave has 
been refracted to the extent that the angle of refraction <£ r 
becomes equal to 90°, the wave will be returned to earth. 


Fig. 6.8 Effect on ionospheric re- 
fraction of angle of incidence and 
frequency of wave 

Should the angle of refraction be less than 90°, the wave will 
emerge from the top of the layer and travel on to a greater 
height. If, then, the wave enters another, higher layer, it will 
experience further refraction and may now be returned to 
earth. If the frequency of the wave is increased, the wave will 
be refracted to a lesser extent and will have to travel further 
through a layer before it is returned to earth. 

30 MHz 

30 MHz 

20 MHz 

Suppose sky waves at frequencies 5, 10, 20 and 30 MHz are 
transmitted and are incident on the lower edge of the E-layer 
with an angle of incidence <^ x (Fig. 6.8). The 5 MHz wave is 
refracted to the greatest extent and is returned to earth after 
penetrating only a little way into the E-layer. The 10 MHz 
wave must penetrate much farther into the E-layer before it is 
returned to earth, while the 20 MHz wave is hardly refracted 
at all by the E-layer and passes on to the Fj-layer. The 
20 MHz wave meets the Fj-layer with a much larger angle of 
incidence, <£ 3 >$ 1 . A smaller change in direction is now re- 
quired to return the wave to earth, and sufficient refraction is 
produced by the F t -layer. The 30 MHz wave is not refracted 
to the extent required to return it to earth and escapes from 
the top of the F 2 -layer. 

If the angle at which the waves are incident on the E-layer is 
reduced to <f> 2 , greater refraction is necessary to return the 
wave to earth. Consequently, only the 5 MHz wave is now 
returned by the E-layer, the 10 MHz and 20 MHz waves 
passing right through and arriving at the Flayer. The refrac- 
tive index of the Fj-layer is lower at 10 MHz than at 20 MHz; 
hence the 10 MHz wave is refracted sufficiently to be returned, 
but the 20 MHz wave is not. The 20 MHz wave passes on to 
the F 2 -layer and is then returned. Once again the 30 MHz 
wave is not returned. 

Further decrease in the angle of incidence of the waves on 
the E-layer may well result in the 20 MHz wave escaping the 
F 2 -layer also and not returning to earth at all, the 5 MHz and 
10 MHz waves being returned by a higher layer. 



An ionospheric layer has a maximum electron density of 6X10 11 
electrons/m 3 . Calculate the maximum frequency that will be returned 
to earth if the angle of incidence is (i) 60°, (ii) 30°. 


(i) From equation (6.2) 

sin 60» = 0.866 =V(l-^^) 

0.75 =1 81X6Xl ° n 
f = 



/= 13.943 MHz (Ans.) 

\l 81x6xl0 11 \ 
(ii) sin 30° = 0.5 = yj (l -5 J 

«„, , 81x6x10" 
0.25 = 1 — 

f = 


/ = 8.05 MHz (Ans.) 

Critical Frequency 

The critical frequency of an ionospheric layer is the maximum 
frequency that can be radiated vertically upwards by a radio 
transmitter and be returned to eartr^fThis condition corres- 
ponds to a wave that travels to the top of the layer, where the 
electron density is at its maximum value, before its angle of 
refraction becomes 90°. The angle of incidence is 0°. There- 
fore, using equation (6.2), 

sin0° = 0=J(l- 81N ^ 



f c % = 81 N m 

(_/«* = Wa^ (6.3) 

The critical frequency of a layer is of interest for two 
reasons: firstly it is a parameter which can be measured from 
the ground and, secondly, it bears a simple relationship to the 
maximum usable frequency of a sky-wave link. 



Maximum Usable Frequency 

The maximum usable frequency (m.u.f.) is the highest fre- 
quency that can be used to establish communication, using the 
sky wave, between two points.! If a higher frequency is used, 
the wave will escape from the top of the layer and the signal 
will not be received at the far end of the link. The m.u.f. is 
determined by both the angle of incidence of the radio wave 
and the critical frequency of the layer; thus 

m.u.f . = fcJcas fa (6.4) 

The m.u.f. is an important parameter in sky-wave propaga- 
tion. Since the attenuation suffered by a wave is inversely 
proportional to the frequency of the wave it is desirable to use 
as high a frequency as possible. 


Calculate the maximum usable frequency of a sky-wave link if the 
angle of incidence is 45° and the maximum electron density of the 
layer used is 4 x 10 11 electrons/m 3 . 


From equation (6.3) 

fen, = 9V(4 x 10") = 5.692 MHz 

Therefore, from equation (6.4) 

m.u.f. = 5.692/cos45° = 8.05MHz (Arts.) 

The electron density of an ionospheric layer is not a con- 
stant quantity but is subject to many fluctuations, some regular 
and predictable and some not. As a consequence the m.u.f. of 
any given route is also subject to considerable variation over a 
period of time. The m.u.f. of a link will vary throughout each 
day as the intensity of the sun's radiation changes. Maximum 
radiation from the sun occurs at noon, while after dark there is 
no radiation. There is always a time lag of some hours between 
a change in the ultra-violet radiation passing through the 
ionosphere and the resulting change in electron density, and so 
the m.u.f. may be expected to vary in the manner shown by 
the typical graphs of Fig. 6.9. 

In addition to the predictable m.u.f. variations, further fluc- 
tuations often take place and, because of this, operation of a 
link at the m.u.f. prevailing at a given time would not produce 
a reliable system/ Usually a frequency of about 85% of the 
m.u.f. is used to operate a sky-wave link. [This frequency is 
known as the optimum working (trafficjfrequency or o.w.f. 
Since the m.u.f. will vary over the working day, the o.w.f. will 
do so also and it is therefore necessary to change the transmit- 
ted f requencyas propagation conditions vary.) The number of 











\ \ 






l \ 











— " '^«n 





2 4 6 8 10 12 14 16 18 20 24(0) 

Time of day (G.M.T.) 

Fig. 6.9 Variations of m.u.f. with time of day 

available frequencies is limited and international frequency 
sharing is necessary. Usually, an individual transmitter is allo- 
cated several carrier frequencies, any one of which can be 
employed if necessary. When propagation conditions are poor, 
it may prove necessary to transmit on more than one fre- 
quency and even, when conditions are particularly bad, to 
re-transmit when conditions improve. 

The attenuation of a sky-wave link increases with decrease 
in the frequency of the transmission and, if the transmitted 
power is maintained at a constant level, the received field 
strength is inversely proportional to frequency. The lowest 
useful frequency (l.u.f .) is the lowest frequency at which a link 
with a given signal-to-noise ratio at the receive aerial can be 
established. The l.u.f. varies with time of day and year in a 
similar manner to the m.u.f. 


£V,^E layerfl 

t53KSfi"*» M 

Fig. 6.10 Skip distance 

Skip Distance 

L There is a minimum distance over which communication at a 
given frequency can be established by means of the sky wave, i 
Usually, the frequency considered is the m.u.f . of the link. If an 
attempt is made to reduce this minimum distance by using a 
smaller angle of incidence, the wave will not be returned to 
earth by the E-layer but will pass through it. This minimum 
distance is known as the skip distance and is shown in Fig. 
6.10. For a given frequency each of the ionospheric layers has 
its particular skip distance. It should be evident from the 
previous discussion that the higher the frequency of the wave 
the greater is the skip distance. 

Multiple-hop Transmissions 

When communication is desired between two points which are 
more than about 4000 km apart, it is necessary to employ two 
or more hops, as shown in Fig. 6.11. The sky wave is refracted 
in the ionosphere and returned to earth, and the downward 
wave is reflected at the surface of the earth to be returned 
skywards. The overall m.u.f. of a multi-hop link is the lowest 
of the m.u.f.s of the individual links. 

Fig. 6.11 Multi-hop transmission of 
sky wave 

The number of hops that are possible depends upon both 
the transmitter power and the losses incurred at each ground 
reflection and ionospheric refraction. The main disadvantage 
of a multi-hop route is the likelihood of pronounced selective 

The Space Wave 

At frequencies in the v.h.f., u.h.f. and s.h.f. bands, the range 
of the surface wave is severely limited and the ionosphere is 
ujmWejQjefracljradiQjvaves. Because the signal wavelength is 
short, the transmitting and receiving aer ials ca n both be instal- 
led at a height of several wavelengths above earth. Then the 


Direct wave 

Reflected wave 

Fig. 6.12 The space wave 

Received field strength 

Fig. 6.13 Variation of field strength 
with height above ground at the 
receive end of a space wave radio 

space wave can be used for communication since its direct and 
reflected waves will not (always) cancel. 

The principle of a space-wave radio link is illustrated by Fig. 
6.12. The direct wave travels in a very nearly straight line 
path, slight refraction being caused by the temperature and 
water vapour gradients in the troposphere. The total field 
strength at the receiving aerial is the phasor sum of the field 
strengths produced by the direct and the reflected waves. The 
received field strength varies with height above ground as 
shown in Fig. 6.13. Obviously, careful choice of the height at 
which the receive aerial is to be mounted is essential. The 
maximum possible distance between the two aerials is some- 
what greater than line-of -sight but, in practice, link lengths 
are shorter than this in order to improve the reliability of the 
system. Most links are some 25-40 km in l ength . 

The direct wave must be well clear of any obstacles, such as 
trees and buildings which might block the path, and this factor 
will determine the necessary aerial heights. 

The majority of point-to-point space wave radio systems are 
of considerably longer route length than 40 km and must of 
necessity require a number of relay stations. The use of relay 
stations will be discussed in Chapter il. 

Propagation via Communication Satellite 

The basic principle of a communication satellite system is 
shown simply in Fig. 6. 14. Since frequencies in the s.h.f . band 
are used in both directions of propagation, the ionosphere has 
negligible effect on the path of the radio waves, and so these 
travel in straight lines. This method of propagation can pro- 
vide wideband multi-channel telephony systems over distances 
of thousands of kilometres with the utmost reliability. 

Tropospheric Scatter Propagation 

Another method of providing a number of radio-telephony 
channels over a long distance is known as tropospheric scatter 
and is illustrated by Fig. 6.15. A high-power radio wave is 
transmitted upwards from the earth and a very small fraction 
of the transmitted energy is forward scattered by the tropos- 
phere and directed downwards towards the earth. This occurs 
at frequencies above about 600 MHz, but particularly at 900 
MHz, 2 GHz and 5 GHz. The forward-scattered energy is 
received by a high-gain aerial, often of the parabolic reflector 
type, to provide a reliable long-distance, wideband, u.h.f . radio 
link.The distance between the transmitting and receiving sta- 
tions is usually in the range of 300 to 500 km and nearly 
always covers geographically hostile terrain, such as moun- 

Fig. 6.14 An earth satellite com- 
munication system 

Fig. 6.15 Scatter propagation 



Ground station 
in North America 

Ground station 
in Europe 

Transmission North America to Europe 

Transmission Europe to North America 

Ionosphere ,^ 

Low-power forward 
scattered beam 

main beam 

tains, jungle or ocean. Since only a small fraction of the 
transmitted power arrives at the aerial, the system is . very 
inefficient and demands the use of high-power transmitters and 
high-gain, low-noise radio receivers. For this reason a 
tropospheric scatter system is only provided when no other 
alternative is available. 


Fading, or changes in the amplitude of a received signal, is of 
two main types: general fading, in which the whole signal fades 
to the same extent; and selective fading, in which some of the 
frequency components of a signal fade while at the same time 
others increase in amplitude. 

General Fading 

As it travels through the ionosphere, a radio wave is at- 
tenuated, but since the ionosphere is in a continual state of 


flux the attenuationjs not constant, an d the amplitude of jhe 
"receTv^d~s!gnarvaries. Under certain conditions a complete 
lade^out of signals may occur for up to two hours. With the 
exception of complete fade-outs, general fading can be com- 
bated by automatic gain control (ajx.) in the radio receiver. 

Path 2 

• v Ionosphere 




Fig. 6.16 Multi-path propagation 

Selective Fading 

The radio waves arriying_at the receiving end of a sky-wave 
radio link may haveftravelled over two or more different p aths 
through the ionosphere (Fig. 6.16a). The tota l field strength at 
the receiving aerial is the vhasor sum of the field strength s 
produced-by^- each _wave. Since the ionosphere is subject to 
"continual fluctuations^in-its ionizatio n density ^ the difference 
between the lengths of paths 1 and 2 will fluctuate and this will 
alter the total field strength at the receiver. Suppose, for 
example, that path 2 is initially one wavelength longer than 
path 1; the field strengths produced by the two waves are then 
in phase and the total field strength is equal to the algebraic 
sum of the individual field strengths. If now a fluctuation 
occurs in the ionosphere causing the difference between the 
lengths of paths 1 and 2 to be reduced to a half -wavelength, 
the individual field strengths become in antiphase and the total 
field strength is given by their algebraic difference. 

The phase difference between the field strengths set up by 
the two waves is a function of frequency and hence the phasor 
sum of the two field strengths is different for each component 
frequency in the signal. This means that jojnejr£qjjenties may 
fade at thejjame in stant a sjQthe rs are augmented ; the effect is 
particularly serious in double-sidebarid ^rnpU^d^nio^ulated 
systems because, if the carrier component fades^to_aJeyel well 
below that of the two sideband.s, the "sfebands^^wjU^eat 
together and considerable signal distortion jvill be produced. 

Selective fading cannot be overcome by the use~bf a^g.c. in 
the receiver since this is operated by the carrier level only. 
Several methods of reducing selective fading do exist. For 
example, the use^ of^|requencies as near to^the^jr| ; ui v as 
possible, the use oflf transmitting aerial that radiates only one 
possible mode of propagation, the use of single-sideband or 
frequency-modulated systems, or the use of a specialized 
equipment as Lincompex. Selective fading of the sky wave is 
most likely when the route length necessitates the use of two 
or more hops. Suppose, for example, that a two-hop link has 
been engineered. Then, because of the directional characteris- 
tics of the transmitting aerial, there may well also be a 
three-hop path over which the transmitted energy is able to 
reach the receiving aerial. 


Selective fading can also arise with systems using the surface 
and space waves. In the daytime the D-layer of the ionosphere 
completely absorbs any energy radiated skywards by a 
medium-wave broadcast aerial. At night the D-layer disap- 
pears and any skywards radiation is returned to earth and will 
interfere with the ground wave, as shown in Fig. 6.166. In the 
regions where the ground and sky waves are present at night, 
rapid fading, caused by fluctuations in the length of the sky 
path, occurs. This is why reception of medium-waveband 
broadcasts is much worse at night than in the daytime; it is 
minimized by the use of transmitting aerials having maximum 
gain along the surface of the earth and radiating minimum 
energy skywards. 

Fig. 6.16c illustrates how multi-path reception of a v.h.f. 
signal can occur. Energy arrives at the receiver by a direct path 
and by reflection from a large object such as a hill or gas- 
holder. If the reflecting object is not stationary the phase 
difference between the two signals will change rapidly and 
rapid fading will occur. 

Use of the Frequency Bands 

_At_fregjjencies in the v.l.f. and L^bands, aerials are very 
ineffici ent and hi gh-power transmitters must be u sgd,. The 
radiated energy is vertically polarized^ and will prop_aga.tejneli- 
^blyTno fading) for thousands of kilometres using the surface 
wave or by means of multiple reflections between ionosphere 
and earth. Services provided in this band are ship-to-shoxe_ 
telejgajjlry^navigation systems, and sound broadcasting (l.f. 
band). In the m.f. band the range of the surface wave is limited 
to some hundreds of kilometres and the main use of the band 
is for sound broadcasting (647-1546 kHz). Also provided are 
ship telephonic and telegraphic links in, respectively, the bands 
405-525 kHz and 1.6-3.8 MHz. 

At high frequencies the main mode of propagation is the sky 
wave, the surface wave giving, if required, service for distances 
of up to the skip distance. The h.f. band is used for interna- 
tional point-to-point radio-telephony links on a number of 
sub-bands, for sound broadcasting, and for marine and aero 
mobile systems. 

In the v.h.f. and higher bands the surface wave has a very 
limited range and the ionosphere (normally) does not return 
waves to earth. The modes of propagation used are therefore 
the space wave and, at certain frequencies in the s.h.f. band, 
the communication satellite. Scatter is also sometimes used. 
Services provided are sound broadcasting in the v.h.f. band 
(88.1-96.8 MHz), land, marine and aero mobile systems in the 
v.h.f. and u.h.f. bands, television broadcasting in the u.h.f. 


band, and point-to-point multi-channel telephony systems in 
the u.h.f. and s.h.f. bands. (Details of the frequencies used are 
given in TSII.) 


6.1. (a) Which ionized regions are present in the atmosphere during 
a summer day? Give the approximate height of each of these 
regions, (ft) What is meant by the following terms in connection 
with ionospheric propagation: (i) maximum usable frequency, (ii) 
gyro-frequency, (c) How is the maximum usable frequency 
related to (i) critical frequency, (ii) angle of incidence, (iii) 
density of ionization of the reflecting layer? (C & G) 

6.2. (a) What is the meaning of the following terms: (i) maximum 
usable frequency, (ii) optimum traffic frequency? (b) How are (i) 
and (ii) related? (c) Explain how a radio wave incident on an 
ionized region is returned to earth by refraction, (d) How does 
the refraction vary with (i) frequency, (ii) electron density in the 
ionized region, (iii) angle of incidence? (C & G) 

6.3. (a) Explain the mode of propagation whereby low radio fre- 
quencies can be used for world-wide communication, (ft) How 
does field strength vary with the distance from the transmitter 
and with radiated frequency? (c) What are the advantages and 
disadvantages of low-frequency propagation? (C & G) 

6.4. Explain the meanings of the following terms: (i) critical fre- 
quency, (ii) selective fading, (iii) surface wave, (iv) ground wave, 
(ft) With what frequency band is each of the above normally 
associated? ( c & G ) 

6.5. (a) Briefly describe the propagation of radio signals by means 
of the ground wave, (ft) Why is the range of a broadcast 
transmitter using the ground wave limited even when the 
ground is lossless? (c) What is the name of the propagation 
mechanism whereby ground waves move around relatively 
small objects? (d) Does loss in the ground wave increase or 
decrease with increase in (i) conductivity, (ii) frequency, (iii) 
permittivity? (C & G) 

6.6. (a) Which ionized regions are present in the atmosphere during 
a winter night? Give the approximate height of each of these 
regions, (ft) What do you understand by the following terms in 
connection with ionospheric propagation: (i) skip distance, (ii) 
gyro-frequency? (c) What is the effect on the skip distance of 
an increase in (i) transmitted frequency, (ii) transmitted power, 
(iii) density of ionization of the reflecting layer? (C & G) 

6.7. (a) Briefly describe what you understand by the terms (i) 
critical frequency, (ii) maximum usable frequency, (iii) optimum 
traffic frequency, (ft) What is the relationship between (i) and 
(ii) in (a)? (c) Fig. 6.17 is a simplified diagram of an ionospheric 
region in the atmosphere: (i) explain how the radio wave 
incident on the ionized region represented in Fig. 6.17 is 
returned to earth when it is below the m.u.f.; (ii) why does a 
wave at a frequency above the m.u.f. penetrate the region? (iii) 
where is the maximum electron density in the ionospheric region 
shown in Fig. 6.17? 

6.8. Explain how selective fading can arise on a long-distance 
short-wave radio link. How can its occurrence be minimized by 
a suitable choice of frequency? Briefly outline some radio 
transmission and reception techniques which reduce the effects 
of selective fading in (a) telephony, (ft) telegraphy. 



. N l 

Layers of 
N 1f N 2 , N 3 

Fig. 6.17 

6.9. Explain why v.h.f. and u.h.f. radio signals can be received 
beyond the line of sight distance from the transmitter. Explain 
why the height above ground of the aerial at the receiving end 
of the link is important. 

6.10. Explain briefly, with the aid of sketches, how multipath inter- 
ference occurs in the following types of radio transmission: (a) 
medium-frequency broadcasting, (b) high-frequency long- 
distance telephony, (c) v.h.f. television broadcasting. In each 
case state methods which are adopted to reduce the effects of 
each form of interference. 

6.11. Explain how a long-distance wideband radio link can be estab- 
lished using tropospheric scatter in the u.h.f. band. A parabolic 
reflector aerial used in a 2 GHz tropospheric scatter system has 
a diameter of 6 m and radiates a power of 1 kW. Calculate the 
effective radiated power. 

Short Exercises 

6.12. List the ionospheric regions which are present in the upper 
atmosphere during a summer night. Give their approximate 

6.13. List the ionospheric regions which are present in the upper 
atmosphere during a winter day. Give their approximate 

6.14. Explain why as high a frequency as possible is used for a h.f. 
sky-wave transmission. 

6 J.5. What is meant by the term gyro-frequency? 

6.16. Explain the meanings of the terms ground wave and surface 
wave used in radio wave propagation. 

6.17. For which frequency bands is the surface wave the main mode 
of propagation? Give typical ranges for each band. 

6.18. Why does the surface wave suffer less attenuation over sea than 
over land? 

6.19. Explain the meanings of the terms critical frequency, maximum 
usable frequency, and lowest useful frequency when used in 
radio propagation work. 

6.20. What is meant by the term skip distance? Does the skip 
distance increase or decrease when the frequency is raised? 

6.21. Give two reasons why a frequency as near the m.u.f. as possible 
is used for a sky-wave radio link. 

6.22. Explain, with the aid of a diagram, why multi-hop sky-wave 
paths are prone to selective fading. 

6.23. Does skip distance increase or decrease if (i) the frequency is 
raised, (ii) the transmitted power is increased, (iii) the electron 
density of the refracting layer is increased? 

7 Radio-frequency 
Power Amplifiers 


Radio-frequency power amplifiers are used in radio transmit- 
ters to amplify the carrier frequency to the wanted power 
output level. The amplifiers are often expected to provide 
frequency multiplication at the same time as power amplifica- 
tion. For many radio transmitters the output power is of the 
order of tens, or perhaps hundreds, of kilowatts and such 
power levels are, at present, beyond the capacity of transistors. 
High-power transmitters therefore employ thermionic valves 
as the active device in the output stage. The earlier stages will 
probably use transistors. On the other hand, a low-power 
transmitter will be completely transistorized. Hence r.f. power 
amplifiers may use a transistor or a valve to provide amplifica- 

The choice between the triode valve and the tetrode valve 
must be made with due regard to a number of factors. The 
tetrode has a larger gain than the triode which means that a 
smaller input voltage is needed to develop a given output 
power. The anode-to-grid capacitance is considerably reduced 
by the screen grid, and usually the tetrode can be operated 
without neutralization circuitry. The triode will need to be 
neutralized, unless it is operated in the earthed grid configura- 
tion, to avoid positive feedback via its anode-grid capacitance. 
It is usually necessary to drive the triode valve into its grid 
current region in order to obtain a sufficiently large output 
power, and this practice results in distortion of the output 
waveform. The tetrode has the disadvantage that power is 
dissipated at its screen grid and so its overall efficiency is 
reduced; also some means of removing this heat may be 

Radio-frequency power amplifiers are operated under either 
Class B or Class C conditions. Class B operation has a max- 
imum theoretical efficiency of 78.5% but can be used to 



amplify an amplitude-modulated signal without the introduc- 
tion of excessive distortion. The Class C amplifier has a higher 
efficiency but it cannot be used to amplify an amplitude- 
modulated signal. The extra efficiency provided by the Class C 
circuit is extremely important in a high-power application. For 
example, to obtain an output power of 100 kW requires an 
input power of 125 kW if the efficiency is 80%, but the input 
power must be 166 kW of the efficiency is reduced to 60%. 
The difference between the input and output powers is a waste 
of power and is dissipated in the valve in the form of heat and 
arrangements must be made to remove it. Even in the case of 
a low-power transmitter the utmost efficiency may still be 
important since such a transmitter may be battery operated. 

The Class C Radio-frequency Power Amplifier 

The basic circuit of a Class C radio-frequency power amplifier 
is given in Figs. 7.1a and b. A triode valve has been shown but 
equally a tetrode could be used. The difference between the 
two circuits shown lies in the way in which the anode-tuned 
circuit has been connected. In the SERIES-FEED circuit of 
Fig. 7.1a the tuned circuit is connected in series with the h.t. 
supply, while in the PARALLEL-FEED circuit of Fig. 7.16 
the tuned circuit is connected in parallel with the valve and is 
isolated from the h.t. supply by the d.c. blocking capacitor C 2 . 
The parallel-feed circuit uses another extra component, 
namely L 4 , which stops r.f . currents entering the power supply 
instead of the tuned circuit C 3 -L 5 . In both circuits the valve is 
biased to operate under Class C conditions by the negative 
bias voltage Vj,. Usually V(, is more than twice the cut-off 
voltage of the valve. The bias voltage is applied via inductor 

+v ht 

c 2 



signal L 1 

Input ., 

signal '•13 l L 2 

*C 3 L 5 \ U 6 

' ± ' 

(a) (b) 

Fig. 7.1 Class C tuned power amplifiers: (a) series fed, (b) 
parallel fed 


+ i 

/, (max) 

Fig. 7.2 Current and voltage 
waveforms in a Class C amplifier 


L 3 to stop signal-frequency currents being shunted, via the 
bias supply, to earth. Capacitor C\ prevents the bias voltage 
being shorted to earth by L 2 . The parallel-feed arrangement 
ensures that the tuned circuit components are at zero d.c. 
potential which makes insulation and safety less of a problem. 

When a sinusoidal voltage is applied to the input terminals 
of the amplifier, the valve will only conduct at the positive 
peaks of the signal voltage (Fig. 7.2). This means that the 
anode current flows as a series of pulses, each of which lasts 
for a time period smaller than one-half the periodic time of the 
input signal waveform. Clearly, the anode current is not 
sinusoidal but consists of a d.c. component, a fundamental 
frequency (equal to the input signal frequency) component, 
plus components at a number of harmonically related frequen- 
cies. The amplitude of the fundamental is greater than that of 
any of the harmonics. The anode circuit is tuned to be reson- 
ant at the signal frequency. A parallel-tuned circuit has its 
maximum impedance at its resonant frequency and this impe- 


dance, known as the DYNAMIC RESISTANCE R d , is a pure 
resistance. At all other frequencies the impedance of a 
parallel-tuned circuit is much smaller and is not purely resisi- 
tive. The voltage developed across the anode circuit is there- 
fore produced only by the fundamental (signal) frequency 
component of the anode current and is of sinusoidal 

Very often with triodes (but not with tetrodes) the grid 
potential is taken positive with respect to the cathode at its 
peak positive half-cycles. This practice does result in the flow 
of grid current but it also produces anode current pulses of 
larger peak value than would otherwise be possible. Since the 
amplitude of the fundamental-frequency component of the 
anode current is proportional to the peak anode current, a 
larger output voltage is thus obtained. 

The anode voltage of the valve is equal to the h.t. supply 
voltage minus the voltage developed across the anode tuned 
circuit and is in antiphase with the grid voltage. The current 
and voltage waveforms at various points in a Class C tuned 
amplifier are shown in Fig. 7.2. The following points should be 

(a) The anode current flows whenever the positive half- 
cycles of the input signal voltage make the grid potential 
less negative than the cut-off voltage of the valve. 

(b) Grid current flows whenever the grid potential is posi- 

(c) The minimum value of the anode voltage occurs at the 
same times as the positive peaks of the input signal 
voltage. It is necessary to ensure that at no time does the 
grid potential become more positive than the minimum 
anode voltage. If this should happen a large grid current 
will flow and damage the valve. 

(d) The circuit has a high anode efficiency because anode 
current flows only at those times when the instantaneous 
anode voltage is at or near its minimum value. This 
reduces the power dissipated at the anode of the valve. 

If the voltage of h.t. supply is increased, the peak value of 
the anode current pulses will increase in the same ratio and 
this, in turn, will increase the signal output voltage. Thus, in a 
Class C tuned amplifier the output voltage is directly propor- 
tional to the h.t. supply voltage. 


Angle of Flow 

The anode current of a Class C tuned power amplifier flows in 
a series of less-than-half sinewave pulses. The conduction time 
is expressed in terms of a parameter known as the ANGLE 
OF FLOW. The anode current flows whenever the total grid 
voltage is less negative than the cut-off voltage of the valve. 
Thus, referring to Fig. 7.3, which shows, in more detail than 
Fig. 7.2c, the grid voltages existing in the circuit, 6 is the angle 
of anode current flow. In this figure V co is the cut-off voltage 
of the valve and V b is the bias voltage applied. Also shown is 
the angle <£ of grid current flow, always <£ < 0. 

Input signal 

Fig. 7.3 Angle of flow 


The angle of flow is always less than 180° (0 = 180° gives 
Class B conditions), the actual value chosen being a compro- 
mise between the conflicting requirements of anode efficiency 
and power output. A reduction in the angle of flow reduces the 
power output of the amplifier but increases its efficiency. 
Generally, the angle of anode current flow is chosen to be 
somewhere in the region of 120°. 

When is approximately 120° the anode current flows for 
only one third of each cycle and the current waveform can be 
considered, without the introduction of undue error, to be of 
triangular shape. This is a convenient assumption to be able to 
make since it allows the mean value of the anode current to be 
easily calculated using equation (7.1): 

*a(mean) ' 

*q(peqk) ^ 




The mean value of the anode current is the direct current 
which is taken from the h.t. power supply. 



The anode current pulses in a Class C tuned amplifier are of approxi- 
mately triangular waveform with a peak value of 3 A and an angle of 
flow of 100°. 
Calculate the mean value of the anode current. 


From equation (7.1) 

3 100 
demean) =-Xrr7: = 0.417 A (Arts.) 

Power Relationships 

The d.c. power supplied by the h.t. power supply to the 
amplifier is equal to the product of the h.t. supply voltage V ht 
and the mean value of the anode current: 

*dc = Vhtla(mean) (7.2) 

Some of this power is dissipated at the anode of the valve and, 
is known as the anode dissipation. The remainder of the input 
power is converted into a.c. power and is delivered to the 
anode tuned circuit. A small amount of this power is dissipated 
in the resistance of the tuned circuit inductance but the rest is 
passed onto the load to provide the power output of the 
amplifier. Normally, the power lost in the tuned circuit is small 
and will be neglected in this book. The a.c. power P^. delivered 
to the anode tuned circuit, i.e. the a.c. output power, is equal 
to the square of the r.m.s. value of the fundamental frequency 
component I a(f) of the anode current times the dynamic resis- 
tance R d of the tuned circuit: 

Pac = laCfiRd (7.3) 

The ANODE EFFICIENCY r\ of a Class C amplifier is the 
ratio PaJPdc expressed as a percentage 

i)=-^xl 00% (7.4) 


Alternatively, the power output of the circuit can be expressed 
in terms of the anode, and h.t. supply voltages. The fundamen- 
tal frequency component of the anode current develops a 
voltage V L sin <at across the tuned circuit, where V L = I a(f) R d . 

The output power can therefore be written as (VjJ2) 2 /R d . 

The anode voltage V a of the valve is V a = V ht — V L sin wt. 

When sin <at = 1 anode voltage is at minimum value V a(min) . 

Then V L = V h( -V a(min) 



.(Vht Vq(min)) 




In a Class C tuned power amplifier the anode current is of approxi- 
mately triangular waveform of peak value 4.6 A and angle of flow 
120°. If the anode efficiency of the circuit is 75% and the h.t. supply 
voltage is 1 kV calculate the output power. 


4.6 120° 
Pdc= T X 360° Xl00 ° 


Pa. = vPdc = 0.75 x 766.7 = 575 W (Arts.) 

Earthed-grid Operation of a Triode Class C Amplifier 

When a triode valve is used in the common-cathode connec- 
tion, feedback of radio-frequency energy from the anode 
(output) circuit to the grid (input) circuit via the anode-grid 
capacitance of the valve will take place. This positive feedback 
will produce instability and possibly unwanted oscillations. To 
overcome the instability problem it will be necessary to use 
extra circuitry, known as NEUTRALIZATION, to cancel or 
neutralize the unwanted feedback. In modern transmitters the 

Fig. 7.4 Earthed grid Class C tuned 
power amplifier 

need for neutralization is overcome by connecting the triode in 
the earthed-grid configuration (Fig. 7.4). The earthed grid now 
acts as a screen between the cathode and anode electrodes 
which reduces the cathode-anode capacitance to a very small 
value. Now unwanted feedback from the output (anode) to 
input (cathode) circuit is at very low level and generally 
neutralization circuitry is not needed. 

Grid Bias 

The valve must be biased to operate under Class C conditions 
and the required bias voltage can be obtained from a separate 





Fig. 7.5 Leaky-grid bias 

power supply as shown in the circuits of Fig. 7.1a and b. An 
alternative arrangement which can be used instead of, or as 
well as, a power supply is the LEAKY-GRID bias circuit. The 
action of a leaky-grid bias circuit, two versions of which are 
shown in Fig. 7.5, has been described elsewhere [EII] but, very 
briefly, the required bias voltage is developed across capacitor 
C t by the flow of grid current. The use of leaky-grid bias has 
the disadvantage that if, for some reason, the input signal 
voltage is removed, the bias voltage will disappear. The valve 
may then pass a very large anode current and quite possibly 
suffer damage. To prevent such an occurrence a small cathode 
resistor can be fitted or some fixed-bias can also be provided. 

Effect of Loading 

The anode tuned circuit must be tuned to the required fre- 
quency of operation and then possess sufficient selectivity to 
be able to discriminate against the harmonic content of the 
anode current. These requirements are satisfied by using an 
inductor of high Q-factor and a low-loss capacitor. In addi- 
tion, the tuned circuit must provide a suitable load impedance 
for the valve and must also transfer the power from the anode 
circuit to the load. The effective resistance of the tuned circuit 
is equal to its dynamic resistance in parallel with a coupled 
resistance. The magnitude of this coupled resistance depends 
upon both the coupling between the anode circuit and the load 
and the load impedance itself. By suitable adjustment of this 
coupling the optimum load for the valve can be obtained. 

The efficiency with which energy is transferred from the 
anode circuit to the load depends upon the ratio (loaded 
Q)/(unloaded Q). This means that the unloaded Q-factor 
should be high but should fall to a low value once the load is 
connected. The Q-factor cannot be permitted to fall to too low 
a figure however or insufficient discrimination against har- 
monics will be provided. Typically, the loaded Q-factor is 
about 12. 

Class B Tuned Power Amplifiers 

The Class C tuned power amplifier has the advantage of a very 
high anode efficiency but it can only be used when the input 
signal voltage is of constant amplitude. If an amplitude- 
modulated signal were applied to the amplifier, considerable 
distortion would be introduced. This reason for this is illus- 
trated by Fig. 7.6 which shows a 75% modulated wave applied 
to a Class C biased valve characteristic. The peaks of the 
modulation envelope produce anode current pulses of varying 
peak value, but during the troughs of the envelope the grid 


Fig. 7.6 Class C amplifier handling 
an amplitude-modulated waveform 


Positive half-cycles 

of input amplitude-modulated 


voltage is unable to drive the valve into conduction. This form 
of distortion can only be prevented by ensuring that all positive 
half-cycles of the input signal voltage, no matter how small, 
cause anode current to flow. This effectively means that the 
bias voltage should be reduced until it is equal to the valve's 
cut-off voltage, i.e. the valve must be operated under Class B 

In practice, the mutual characteristics of a valve tend to be 
non-linear for the lower values of anode current and it is 
usual, in order to minimize distortion caused by this non- 
linearity, to use projected grid bias, as shown in Fig. 7.7. The 
valve is not now operated under true Class B conditions since 
a small anode current will flow for zero input signal voltage, 
but little error is introduced in calculation by assuming that 


Fig. 7.7 Projected Class B bias 

Grid voltage 



Fig. 7.8 Anode current waveform 
in a Class B amplifier 

Class B bias is used. The circuit of a linear Class B tuned 
amplifier is the same as given earlier for Class C circuits but 
leaky-grid bias cannot be used. 

When a sinusoidal voltage is applied to a Class B tuned 
amplifier, the anode current will flow as a series of half- 
sinewave pulses (Fig. 7.8) of peak value 4 (max ). The funda- 
mental frequency component of this current will develop a 
voltage V L across the anode tuned circuit. The mean value of 
this current is I aimax )lir and the peak value of its fundamental 
frequency component is I a ( ma x)/2. A number of components at 
other frequencies are also present in the current waveform 
but they will have little contribution to make to the output 

The d.c. power taken from the h.t. supply is 


L a(max) 


The a.c. power output is 

Ja(mox) Vl. 
2V2 V2 


Fac ~ 2V2 V2 


\Mtt Ki(min)) 


The anode efficiency 17 of a Class B tuned amplifier is the ratio 
(PJPdc) x 100% . Therefore 


»J ~. ( Vht - Vaimin)) X T 

a (max) Y hx 

= ^(l— %=^xlOO% (7.7) 

4\ V ht J 

Maximum anode efficiency is obtained when the voltage 
developed across the anode tuned circuit has its maximum 
possible value. This occurs when the valve is driven so that its 
anode voltage varies between zero and twice the h.t. supply 
voltage so that V L = V ht . Then V aimin) = and 

Un«x = Jx 100% = 78.5% (7.8) 

Practical efficiencies must fall short of this figure because 
varying the anode voltage over such a wide range of values 
would lead to considerable signal distortion. Generally, Class 
B tuned amplifiers have an anode efficiency in the region of 
35-45% when amplifying a sinusoidal signal. The anode effi- 
ciency will rise when an amplitude-modulated wave is amp- 
lified by about 10%. 


A Class B tuned power amplifier operates with a h.t. voltage of 1000 
V and a peak anode current of 6 A. If the effective dynamic 
resistance of the anode tuned circuit is 200 il calculate (a) the output 
power and (fc) the anode efficiency of the amplifier. 


(a) The fundamental frequency component of the anode current has a 

peak value of 6/2 = 3 A. 



200 = 900 W (Ans.) 

(b) The mean anode current = 6/ it A and the power taken from the 
h.t. supply is 6000/ -it W. Therefore, 

^ = T^r x 100% = 47 - 1% ( Ans -) 


The Class B tuned power amplifier is often operated in the 
earthed grid configuration both to avoid neutralization and 
because of its improved linearity. 


In the amplifier of Example 7.3 the input signal is amplitude mod- 
ulated to a depth of 60%. Calculate the anode efficiency of the 


From equation (1.9), 


Total output power = 900 (1 +|0.6 2 ) = 1062 W 
The d.c. power taken from the supply is unchanged and so 



x 100% =55.6% (Ans.) 

Transistor Tuned Power Amplifiers 

The transistor versions of the Class B and Class C tuned power 
amplifiers are used in low-power radio transmitters, in particu- 
lar for those in mobile systems. The circuit of a transistor Class 
C tuned power amplifier is shown in Fig. 7.9. Leaky-base bias 
[EII] is provided by 1?! and C 2 with L 3 acting to prevent 

i C3 

— o 



Fig. 7.9 Transistor Class C tuned „_ 


signal-frequency currents passing to earth via C 2 . Alterna- 
tively, a separate bias supply could be used. The collector 
tuned circuit C 4 -L 5 is series fed and coupled by mutual induc- 
tance to the load R L . The anode circuit is tapped to obtain the 
optimum load impedance for T x . Inductor L 4 prevents r.f. 
currents passing into the power supply and C 3 is a decoupling 
component. The circuit of a Class B transistor tuned power 
amplifier is very similar to the circuit of Fig. 7.9 but a separate 
base bias supply voltage must be provided to give slight 
forward bias; otherwise the transistor base/emitter junction of 
the transistor will develop a self -bias that would give Class C 

When a transistor tuned power amplifier is designed for 
operation in the v.h.f. or u.h.f. bands, it is usually expected to 
work between 50fi source and load impedances. This imped- 
ance is not a suitable value for a v.h.f. or u.h.f. transistor to 
work in between, and often input and output T and/or it 
matching networks are used to obtain more convenient values. 


Fig. 7.10 Transistor Class C tuned o 
amplifier with tt coupling to load 

o It 

A typical v.h.f . Class C power amplifier circuit is shown in Fig. 
7.10. Capacitors C u C 2 and C 3 form the input T matching 
network and convert, at the design frequency, the 50 Cl source 
impedance into the source impedance required by the transis- 
tor. C 4 and R 1 provide leaky-base Class C bias and inductors 
L t and L 2 are r.f. chokes which prevent the passage of r.f. 
currents. C 5 is a d.c. blocking component and C 6 , C 7 and L 3 
provide a -n- matching network which converts the 50 fl load 
impedance into the correct impedance for T x to work into. 


A Class C transistor tuned power amplifier operates from a 30 V 
collector supply. If the collector dissipation of the transistor is 1.2 W 
and the mean collector current is 0.1 A determine (a) the a.c. output 
power, (b) the collector efficiency of the amplifier. 


(a) P,* =30x0.1 = 3 W 

Pac = Pdc - collector dissipation = 3-1. 2=1. 8 W (Ans.) 

(b) tj= = 60% 

Frequency Multipliers 

The anode or collector current of a Class C tuned amplifier 
flows as a series of less-than-half sinewave pulses and contains 
components at the input signal frequency and at harmonics of 
that frequency. If the anode or collector tuned circuit is tuned 
to be resonant at a particular harmonic of the input signal 
frequency, the voltage developed across the load will be at that 
harmonic frequency. The angle of flow should be chosen as 
180°/n where n is the order of the harmonic required. Thus, if 
a frequency tripler is to be designed, the angle of flow should 
be 60°. The higher the order of harmonic selected by 


the anode (collector) tuned circuit the smaller will be the angle 
of flow and thus the smaller will be the output power. In 
practice, the frequency multiplication obtained is rarely in 
excess of 5. When a larger multiplying factor is wanted two or 
more frequency multipliers are connected in cascade. 

Anode-modulated Class C Tuned Amplifiers 

The output voltage of a Class C tuned power amplifier is 
directly proportional to the h.t. supply voltage. If the h.t. 
supply voltage is increased by, say, 50% the amplitude of the 
voltage developed across the anode tuned circuit also increases 
by 50% . This means that if the h.t. supply voltage is caused to 
vary in sympathy with a modulating signal voltage, the a.c. 
voltage developed across anode tuned circuit will be amplitude 

Class B 

audio-frequency • 


Fig. 7.11 Anode-modulation of a 
Class C amplifier o 

Vht + V m s\n Mm t / 

The h.t. voltage applied to the anode of a Class C tuned 
power amplifier can best be varied by introducing the modulat- 
ing signal into the anode circuit by means of a transformer as 
shown in Fig. 7.11. The total voltage applied to the anode of 
Vi is the sum of the h.t. supply voltage V ht and the modulating 
signal voltage V m sin &> m f which appears across inductor L 6 . 
The maximum voltage applied to the anode of Vj is V ht + V m 
and the minimum voltage is V ht — V m . The depth of modula- 
tion of the output voltage waveform depends upon the relative 
voltages of the h.t. supply and the modulating signal. If, for 
example, V m = V h J2 the depth of modulation will be 50% . 

The modulating signal voltage is produced by an audio- 
frequency power amplifier. Sometimes this circuit may be 
operated under Class A conditions but, for high-power appli- 
cations, it is always a Class B push-pull amplifier [EIII]. The 



Fig. 7.12 The 

Class C amplifier 


6 Carrier 

basic circuit of a Class B modulator and its associated anode- 
modulated Class C amplifier is shown in Fig. 7.12. 

Triodes V x and V 2 are connected in push-pull and operated 
very nearly under Class B conditions; a small forward bias 
voltage V bl is provided via L 4 . L 4 , L 10 and L u are r.f. chokes. 
The modulating signal is first applied to inductor Lj and, since 
L 2 and L 3 are the two halves of a centre-tapped secondary 
winding, then applied in antiphase to the grids of V x and V 2 . 
The action of the push-pull circuit produces an amplified 
version of the modulating signal voltage across L 7 . Thus, the 
effective h.t. voltage applied to the Class C amplifier is V ht + 
V m sin o) m t. Leaky-grid bias, augmented by the bias supply 
V b2 , is provided by C 3 and J?j while C 4 functions merely as a 
d.c. blocking component. 

When there is no modulating signal applied to the circuit, 
the voltage applied to the anode of V 3 is the h.t. supply 
voltage V ht and the output voltage developed across the load is 
of constant amplitude. The power output of the amplifier is the 
unmodulated carrier power. This means that the carrier power 
is equal to the d.c. power supplied to the Class C amplifier 
times its anode efficiency. 

When a modulating signal is applied, the h.t. voltage sup- 
plied to V 3 is varied in accordance with its characteristics and 
an amplitude-modulated waveform is produced across the 
load. The power developed across the load resistance has 


increased by an amount equal to the power contained in the 
upper and lower sidebands. This extra power must have been 
supplied by the modulator stage. Hence in an anode mod- 
ulated Class C amplifier: 

(a) The carrier power output is equal to the d.c. power 
supplied to the Class C amplifier times the efficiency of 
the amplifier. 

(b) The sideband power output is equal to the power pro- 
vided by the Class B modulator times the efficiency of 
the Class C stage. The output power of the Class B 
modulator is equal to the d.c. power supplied to the 
modulator times the efficiency of the modulator. This 
means that the sideband power is equal to the d.c. power 
input to the Class B stage times the product of the anode 
efficiencies of the Class B and Class C stages. 


A Class C anode-modulated amplifier uses a Class C stage with an 
anode efficiency of 75% and a Class B stage whose anode efficiency is 
50%. The sinusoidally modulated output wave form has a depth of 
modulation of 50% and a total power of 1520 watts. Calculate the 
d.c. power supplied to (a) the Class C stage, (b) the Class B stage. 


From equation (1.9) 

Total power P, = 1520 = P C (1 + 10.5 2 ) 

P c = 1520/1.125 = 1351 W 

Total sidefrequency power= 1520- 1351 = 169 W 
(a) D.C. power supplied to the Class C stage is 

ftc(o = 1351/0.75 = 1801.3 W (Arts.) 
(ft) Sidefrequency power supplied to the Class C stage is 

P SF = 169/0.75 = 225.3 W 
Therefore, d.c. power supplied to the Class B stage is 

P dc(B) = 225.3/0.5= 450.6 W (Ans.) 

The depth of modulation of the output amplitude- 
modulated waveform depends upon the amplitude of the mod- 
ulating signal voltage introduced in series with the h.t. supply 
voltage of the Class C stage. For 100% modulation the mod- 
ulating signal voltage must be equal to the h.t. voltage so that 
the effective h.t. voltage for the Class C stage varies between 
and 2V ht . 

The grid bias voltage must be provided wholly, or at least 
mainly, by means of a leaky-grid bias circuit. If, using fixed 
bias, the circuit is adjusted to function correctly as a Class C 
amplifier when the effective h.t. voltage is twice the d.c. supply 
voltage, then during the troughs of the modulation cycle the 


O-Vj, (class B) 

?+V hl 


Fig. 7.13 Push-pull anode-modu- 
lated Class C amplifier 

-V b (class C) 

instantaneous anode voltage will be so small that an excessive 
grid current flows. If leaky-grid bias is used, the bias voltage 
will vary throughout the modulation cycle and maintain the 
correct bias for the instantaneous h.t. voltage. 

Sometimes to increase the power output a push-pull Class C 
stage is used; a typical circuit is shown in Fig. 7.13. 

Collector-modulated Class C Tuned Amplifiers 

A d.s.b. amplitude-modulated wave can be generated by 
collector-modulating a transistor Class C tuned amplifier. The 
modulating signal is introduced in series with the collector 
supply voltage to modulate the voltage applied to the amp- 
lifier. The basic circuit of a collector-modulated Class C amp- 
lifier is given by Fig. 7.14. Transistors T! and T 2 form a 
push-pull amplifier which operates very nearly in Class B, a 
small forward bias being given by the potential divider R t + 
R 2 . The modulating signal voltage is developed across L 6 and 
so appears in series with the collector supply voltage E cc . 
Transistor T 3 operates in Class C with leaky-base bias pro- 
vided by R3-C3 and uses a ir-type network to couple the 
output voltage to the load. 

If a high depth of modulation is required, one stage of 
modulation is likely to prove insufficient. Then the penultimate 
Class C amplifier must also be modulated and Fig. 7.15 shows a 
possible circuit. The collector supply voltage to both the 


Modulating . 
signal 1 

Fig. 7.14 The collector-modulated 
Class C amplifier 

penultimate T 3 and the final T 4 Class C amplifiers passes 
through the inductor L 3 . Both Class C amplifiers are therefore 
collector modulated by the push-pull modulator T 1 fT 2 . The 
Class C stages are shown with T and tt input and output 
coupling networks. Capacitors C 3 , C 6 and C 8 are d.c. blocking 
components, Q and C 5 are decoupling capacitors, and induc- 
tors L 6 and L 9 act as the collector load impedances. Finally, 
the necessary base bias voltages are provided by resistors R 2 

Fig. 7.15 Collector modulation of 
final and penultimate Class C trans- 
istor stages 


and R 3 , the associated inductors L 5 and L 8 preventing r.f. 
currents passing to earth. 

V.H.F. Techniques 

At frequencies in the v.h.f. band the design and construction 
of a tuned power amplifier is more difficult than at lower 
frequencies. Most v.h.f. communication transmitters are low- 
powered and use transistor power amplifiers; in this section 
the use of a transistor circuit is assumed but most of the 
measures mentioned apply equally well to a valve circuit. 

V.H.F. circuits are normally designed to work between 50 ft 
impedances and so input and output coupling networks are 
needed to convert 50 ft into the values between which the 
transistor itself must work. Because of internal feedback a 
transistor may be capable of self-oscillation when connected 
between particular source and load impedances. A transistor 
will be stable and not prone to oscillate if it is connected 
between source and load impedances somewhat lower than the 
matched impedances required for maximum power gain. Be- 
cause of the impedance values concerned, the input and output 
coupling circuits are always either T or w networks as shown 
in Figs. 7.14 and 7.15. Of course, the transistor used should be 
a v.h.f. type designed to have minimum internal feedback, 
adequate current gain, and minimum noise at the operating 
frequency. The inductance of the lead joining the emitter 
electrode to the emitter pin can have an appreciable reactance 
at the higher end of the v.h.f. band and particularly in the 
u.h.f . band. This reactance will cause negative feedback to be 
applied to the circuit and also a non-power dissipating resis- 
tance to appear across its base-emitter terminals; both effects 
reduce its gain. Some transistors are manufactured with a 
multiple-wire emitter lead to minimize this emitter inductance. 

At v.h.f. the reactances of the various stray capacitances in 
an amplifier circuit are low and can adversely affect the circuit 
operation. To minimize the magnitudes of the stray capaci- 
tances the layout of the circuit components must be carefully 
considered and carried out. The components of a circuit must 
be mounted as close to one another as possible so that all 
connections are of minimum length. Leads should cross one 
another at right angles. Some semiconductor manufacturers 
have modules available in which all components are miniature 
types and are very closely packed together. Usually fault 
finding on a module is not really practicable and when faulty 
the module should be discarded and replaced by another in 
working order. Often, a printed circuit board is used for much 
of the circuitry and this reduces the stray capacitance problem. 
When a lead passes from one side to the other of the chassis, 
or a metal screening can, a feedthrough capacitor should be 




Fig. 7.16 


Equivalent circuit of an 

The components used in a v.h.f. amplifier must all be chosen 
with some care. All resistors possess both self -inductance and 
self-capacitance, all inductors possess resistance and capaci- 
tance, and all capacitors have both inductive and resistive 
components. If a component is used at a frequency higher than 
it was designed for, it may not provide the electrical charac- 
teristics expected. For example, Fig. 7.16 shows the electrical 
equivalent circuit of an inductor, and Q represents its self- 
capacitance. At some particular frequency the inductor will be 
self -resonant and act like a high-value resistor; at higher 
frequencies the component will have an effective capacitance. 
Clearly, an inductor must be operated at frequencies well 
below its self-resonant frequency. 

The various stages in a circuit should be positioned in as 
near a straight line as possible and be individually screened. 
To avoid unwanted couplings between different parts of a 
circuit arising from currents flowing in the chassis and/or the 
earth line, all earth connections in one stage should be made to 
a common point. A separate common point should be used for 
each stage. 


7.1. (a) A point-to-point high power communication receiver has its 
r.f. output stage modulated by a push-pull class B modulator. 
Sketch the circuit of the modulator and r.f. output stage, (b) 
The power output of an a.m. anode-modulated transmitter is 
1245 W. The efficiency of the final stage is 60%. If the 
modulation depth is 0.7 and the efficiency of the modulator is 
50%, calculate (i) the modulation power supplied to the anode 
of the final stage, (ii) the anode dissipation of the modulator 
stage. Ignore losses in the modulation transformer. (C & G) 

7.2. (a) Draw the circuit diagram of a push-pull Class B modulator 
with its associated Class C r.f. amplifier, (b) A push-pull Class 
B modulator is used to modulate sinusoidally a push-pull Class 
C r.f. amplifier. The maximum anode dissipation of the r.f. 
amplifier is 250 W and its anode efficiency is 75%. The Class B 
modulator has an anode efficiency of 60% and a maximum 
anode dissipation of 200 W. (i) Calculate the maximum mod- 
ulated r.f. output from the Class C amplifier, (ii) What is the 
maximum modulation power that the modulator can supply to 
the r.f. amplifier? (iii) What is the maximum depth of modula- 
tion? (C & G) 

7.3. Explain briefly how a Class C amplifier may be used as a 
frequency multiplier. Illustrate your answer by waveforms of 
collector voltage, collector current, base voltage, and base 
current. Indicate how the harmonic number of a multiplier 
influences the choice of (a) angle of collector current flow and 
(b) collector load impedance. 

7.4. Draw the circuit diagram of the output stage of a high- 
frequency telephony transmitter using high-power modulation, 
and explain the operation of the circuit. Briefly discuss the 
relative merits of high-power and low-power modulation. 


+750 V 


Fig. 7.17 






Class B 

Class C 





Fig. 7.18 

7.5. Draw the circuit diagram of a Class C tuned power amplifier 
which uses a p-n-p transistor as the active device and is 
designed to operate between source and load impedances of 
50 ft. Explain the operation of the circuit. 

7.6. Fig. 7.17 is the circuit diagram of the output stage of an s.s.b. 

(a) Why is fixed bias used instead of automatic bias? (b) The Tt 
filter minimizes the radiation of harmonics. What is the cause of 
these harmonics? (c) What is the purpose of the meter at Y? 
(d) How is the aerial ammeter connected? (e) How is the it 
filter adjusted to match the amplifier to the aerial? (/) What is 
the purpose of the meter at X? (g) What would be the effect of 
an open-circuited D 2 ? (h) Why is resistor R 2 connected across 
the inductor L 4 ? (i) What is the purpose of R^ (/) What factors 
determine the peak voltage at the aerial output terminal? 


7.7. (a) Make a list of the components of the collector-modulated 
Class C amplifiers of Fig. 7.14 and for each one state its 
function, (b) Describe the operation of the circuit. 

7.8. Fig. 7.18 shows the block diagram of an anode-modulated 
Class C tuned amplifier. 

(a) The efficiencies of the Class B and Class C stages are, 
respectively, 48% and 66%, and the output waveform has a 
depth of modulation of 60% . If the total output power is 1 1 kW 
calculate the d.c. power inputs to the two stages. 

(b) The output from such a circuit has a total power of 30 kW 
and a modulation depth of 70%. If the Class C stage has an 
efficiency of 70% calculate the efficiency of the Class B mod- 


Short Exercises 
7.9. A Class C r.f. amplifier has an angle of flow of 130°. Sketch the 
variation with time of its collector and base voltage over one 
cycle of the sinusoidal applied voltage. Show on your sketch the 
base bias voltage and the base cut-off voltage. 

7.10. With the aid of suitable mutual characteristics explain the 
difference between Class A, Class B and Class C operation in 
an amplifier stage. 

7.11. The collector current in a Class C amplifier has a peak value 
of 5 A, an angle of flow of 120° and is of triangular waveform. 
Calculate the mean value of the current. 

7.12. Draw the circuit of a series-fed collector-modulated Class C 
tuned amplifier. 

7.13. Why are triodes in Class C tuned amplifiers often driven into 
the grid current region while tetrodes are not? 

7.14. The d.c. power taken from the 2000 V h.t. supply of a tuned 
amplifier is 1000 W. Determine the peak value of the anode 
current pulses if the amplifier is operated under (i) Class B and 
(ii) Class C conditions. 

7.15. The a.c. power output of a tuned amplifier is 500 W. If the 
anode efficiency of the circuit is 70% calculate its anode 

7.16. Draw the circuit diagram of an earthed-grid Class B tuned 
power amplifier. State the purpose of each component shown. 

7.17. Explain briefly, with the aid of a sketch, why amplitude- 
modulated signals cannot be handled by a Class C tuned 

7.18. List the functions of a tuned power amplifier. 

7.19. (a) Why does the collector current of a Class C amplifier flow 
as a series of less-than-half sinewave pulses? (b) Why is it that 
the output voltage waveform is not severely distorted? 


Radio Transmitters 


The purpose of any radiocommunication system is to transmit 
intelligence from one point to another; the communication 
may be unidirectional as in the case of sound and television 
broadcasting or it may be bi-directional as with most radio- 
telephony systems. At the transmitting end of the system the 
signal must modulate a suitable carrier frequency to translate 
the signal to the allocated part of the frequency spectrum, and 
then be amplified to the necessary transmitted power level. 

In the v.h.f. and u.h.f . bands both amplitude and frequency- 
modulation transmitters are used but in the lower frequency 
bands only amplitude modulation finds application. Sound 
broadcast transmitters use d.s.b. amplitude modulation but 
radio-telephony systems use either single or independent- 
sideband operation. High-frequency communication transmit- 
ters must be able to alter frequency rapidly as ionospheric 
propagation conditions change in order to maintain a reliable 
service. Modern h.f. transmitters are designed to be self-tuning 
to facilitate the frequency-changing process. 

Amplitude-modulation Transmitters 

In an amplitude-modulated radio transmitter, the carrier wave 
is generated by a high-stability crystal oscillator or a frequency 
synthesizer, and then amplified, and perhaps frequency multi- 
plied, before it is applied to the aerial feeder. At some stage in 
the process the carrier is amplitude-modulated by the informa- 
tion signal. The modulation can be carried out when the 
carrier is at a low level or after it has been amplified to a high 
power level and transmitters are broadly divided into two 
classes, namely low-level and high-level, for that reason. 

The block diagram of a HIGH-LEVEL TRANSMITTER is 
given by Fig. 8.1. The carrier frequency is generated by the 



Class C 


Fig. 8.1 High-level amplitude mod- modulating- 
ulation transmitter signal 

Class C 



Class A 



class C 

Class B 



carrier wave 


Fig. 8.2 Low-level amplitude mod- 
ulation transmitter 

crystal oscillator and is amplified to the level necessary to fully 
drive the output stage by a number of Class C tuned r.f. 
amplifiers. One or more of these amplifiers may be operated as 
frequency multipliers. The modulating signal is amplified by 
the Class A a.f. amplifier and then applied to the Class B 
modulator. The output of the modulator is connected in the 
anode circuit of the final Class C stage and amplitude- 
modulates the amplified carrier wave. The frequency stability 
of the transmitter is dependent upon the stability of the crystal 
oscillator. Since this is generally improved if overtone opera- 
tion of the crystal can be avoided, it is often the practice to 
operate the crystal at its fundamental frequency and use the 
appropriate frequency multiplication to obtain the required 
carrier frequency. A modern practice which can sometimes be 
used is the use of a crystal oscillator at a higher frequency than 
the required carrier and to use frequency division; an im- 
proved frequency stability can then be achieved. 

The advantage of the high-level method of operating a radio 
transmitter is that high-efficiency Class C tuned amplifiers can 
be used throughout the r.f. section. The disadvantage is that 
the a.f. modulating signal must be amplified to a high power 
level if it is to adequately modulate the carrier. This demands 
the use of a high-power Class B a.f. amplifier and this, mainly 
because of the output transformer requirements, is an expen- 
sive item of equipment. When the method is used in a low- 
power transistorized mobile transmitter, this disadvantage 
tends to disappear. High-level modulation is used for d.s.b. 
amplitude-modulated sound broadcast, and v.h.f/u.h.f. mobile 

The LOW-LEVEL method of operating an amplitude- 
modulation transmitter is shown in Fig. 8.2. The carrier vol- 
tage receives little, if any, amplification before it is modulated 
by the signal. The amplitude-modulated wave is then amplified 



Class B 




carrier wave 


ting signal 

Class A 




signal (s) 

Fig. 8.3 






Low-level s.s.b./i.s.b. trans- 

by one or more linear Class B r.f. power amplifiers to the 
wanted output power level. In general, Class C tuned amp- 
lifiers cannot amplify amplitude-modulated waveforms without 
generating excessive distortion. Some modern low-level trans- 
mitters use Class C amplifiers with envelope negative feedback 
to reduce the distortion. The low-level transmitter does not 
require a large a.f. modulating power, which simplifies the 
design of the a.f. amplifiers. On the other hand compared with 
high-level operation its overall efficiency is much lower be- 
cause Class B amplifiers are used in place of Class C circuits. 

The majority of d.s.b. amplitude-modulation transmitters 
use the high-level method of modulation mainly because of the 
greater efficiency offered. The low-level method of operation 
is widely used for s.s.b. and i.s.b. transmitters, the modulation 
process being carried out in a separate drive unit (Fig. 8.3). 
The audio-frequency signal is applied to the drive unit and is 
there converted into an s.s.b. or i.s.b. waveform which is then 
passed on to the main transmitter. In the main transmitter the 
s.s.b./i.s.b. signal is amplified to the required power level and 
translated to the appropriate part of the frequency spectrum. 
The h.f . communication i.s.b. transmitters used in the U.K. for 
international radio-telephony links use a standard drive unit, 
and all variations in transmitted frequency and/or power are 
provided by the main transmitter. 

100-106 kHz 

Audio input A 



0-6 kHz" 


^00 k 



100 kH 





100 kHz 









'100 k 




3.094-3.106 MHz 

h 2 

Audio'input B 



0-6 kHz 



To main 
' transmitter 

94-100 kHz 

Fig. 8.4 Drive unit of an i.s.b. transmitter 

The block diagram of the standard DRIVE UNIT is given in 
Fig. 8.4. The audio input signal to a channel is applied to a 
balanced modulator together with a 100 kHz carrier signal, 
and the wanted sideband, upper for channel A and lower for 
channel B, is selected by the channel filter. The outputs of the 
two filters are combined in the hybrid coil and then passed 
through a 100 kHz stop filter. This filter is provided to remove 
any carrier leak that may be present at the outputs. If required 
at the receiver a low-level pilot carrier is then reinserted into 
the composite signal, the function of this pilot carrier being to 
operate the automatic gain control and automatic frequency 


Fig. 8.5 Method of deriving four 
a.f. channels for transmission over 
an i.s.b. system 

control circuitry in the receiver. The 94-106 kHz i.s.b. signal is 
then translated to the band 3.094-3.106 MHz by modulation 
of the 3 MHz carrier. The output of the drive unit is passed to 
the main radio transmitter for radiation at the required fre- 
quency somewhere in the band 4-30 MHz. 

Since the required bandwidth for a speech circuit is approxi- 
mately 3 kHz, each 6 kHz sideband is capable of accommodat- 
ing two speech channels. Telegraphy signals require an even 
narrower bandwidth, and so several telegraph channels can be 
accommodated in the place of one or more speech channels. The 
method generally employed for obtaining four 3 kHz tele- 
phony channels for application to the channel A and B input 
terminals of the i.s.b. drive unit is shown in Fig. 8.5. Fig. 8.5a 
shows the transmitting-end equipment while Fig. 8.5b shows 
the equipment required at the receiving end. The equipment is 
not usually located at the site of the radio transmitter but is 
installed at the radio telephony terminal, and each pair of 
channels, in the band 250-6000 Hz, is sent to the transmitter 
over a four-wire line circuit. 

0.25-3 kHz 

3.25-6 kHz Ch. A 

3.25-6 kHz 

0.25-3 kHz 





input __ 




Ch. 1 

Ch. A 

Ch. 1 




Ch. B 




6.25 kHz 


6.25 kHz 

0.25-3 kHz 



3.25-6 kHz 

3.25-6 kHz 


0.25-3 kHz 









i— 3 1 






Ch. 2 

Ch. B 

Ch. 2 






Ch. 3 




Ch. 3 

Ch. 4 

Ch. 4 



The block diagram of the drive unit for a s.s.b.s.c. transmit- 
ter is given, with typical frequencies at each point, in Fig. 8.6; 
transmitters of this kind are used in maritime mobile systems. 
A pilot carrier version of the unit is also possible, the pilot 
being added to the s.s.b. signal in the same way as in Fig. 8.4. 

3.097-3.1 MHz 

Fig. 8.6 Drive 

unit of an 


97-100 kHz 




0-3 kHz 




100 kHz 


To main 




3 MHz 


From drive 

3.094-3.106 MHz- 
say3.1 MHz 

Communication transmitters operating in the hi. band must 
be capable of rapid and frequent changes in operating fre- 
quency as ionospheric propagation conditions vary. If the 
tuning and loading process is carried out manually (described 
later in this chapter) it may take 20 minutes or so to complete 
the procedure and for this reason many modern transmitters 
are self-tuning. With a self -tuning transmitter the operator has 
merely to reset some dials at a control position and the 

" feeder 

Fig. 8.7 A self-tuning transmitter 

3.1 MHz 

4-27.5 Mh 







tuned earthed 
grid class B 

n 7.1-30.6MHz 









tuning/loading process is carried out automatically in about 
20-30 seconds. The simplified block schematic diagram of a 
SELF-TUNING TRANSMITTER is shown in Fig. 8.7. The 
i.s.b. output of the drive unit shown in Fig. 8.4 is first amplified 
and then frequency translated to its allocated carrier frequency 
in the band 4-27.5 MHz. The translation process is carried out 
by mixing the i.s.b. signal with the appropriate frequency in 
the band 7.1-30.6 MHz. The mixing frequencies are derived 
from a FREQUENCY SYNTHESIZER. The difference fre- 
quency component of the mixer output waveform is selected, 
and amplified, by several cascaded tuned amplifiers, to the 
voltage required to drive the earthed-grid Class B output stage 
to give the rated output power. The tuned amplifiers and the 
Class B stage are tuned automatically by motor-driven vari- 
able inductors and capacitors. 

Fig. 8.8 


Another self-tuning trans- 

From drive unit 

4-27 MHz 


Class B tuned 
power amplifier 

* feeder 

control circuitry 

Another version of the self -tuning transmitter (Fig. 8.8) 
employs a wideband amplifier which does not require tuning in 
order to amplify the signal provided by the drive unit to the 
level necessary to operate the tuned power output amplifier. 
The wideband amplifier operates over the entire frequency 
band covered by the transmitter. The drive unit for this 
transmitter must be able to produce the i.s.b. or s.s.b. signal at 
the desired frequency of operation and hence differs from the 


unit of Fig. 8.4 in that its output frequency is not constant. The 
output frequency of the drive unit, and thus of the transmitter, 
is determined by a frequency synthesizer. When the transmit- 
ted frequency is to be altered, the synthesizer is set to generate 
the appropriate frequency which, after mixing with the 
i.s.b./s.s.b. signal, produces a signal at the new wanted fre- 
quency. The tuning and loading of the tuned Class B output 
stage is automatically adjusted to the correct value in about 30 

The power output of a self -tuning h.f . transmitter is several 
kilowatts, typically 20 kW. 

A self -tuning transmitter may be called upon to work at any 
frequency in the band 4-27.5 MHz. Since this is a wider 
bandwidth than a rhombic or a log-periodic aerial can effi- 
ciently work over, some kind of aerial switching is often used 










From other 

To other 


600 O 
two-wire feeder 


Rhombic or log-periodic 

Radio station building 

Fig. 8.9 Use of an aerial exchange 

and Fig. 8.9 illustrates a possible arrangement. A number of 
transmitters are connected to the aerial exchange; this is a 
switching array that makes it possible for any of the transmit- 
ters to be switched to any particular aerial. 

Output Stages 

The output stage of a h.f. transmitter must be designed to 
satisfy a number of requirements which are listed below: 

(a) It must transfer the wanted output power to the aerial 
feeder with the utmost efficiency. 

(b) It must have sufficient selectivity to discriminate against 
the unwanted harmonic components of the anode cur- 
rent, but not against the side frequencies of the signal. 

(c) It should operate in a stable and linear manner. 

(d) Tuning the stage to the required operating frequency 
and optimizing its coupling to the aerial feeder should be 
as easy and rapid a process as possible. Often this 
process is carried out automatically. 

— Output 

(50 «) 

Fig. 8.10 Output stage of an 
earthed-grid Class B tuned amplifier 
(From Post Office Electrical En- 
gineers' Journal) 

Fig. 8.11 Method of coupling a 
push-pull output stage to a balanced 
feeder (From Post Office Electrical 
Engineers' Journal) 

Tank .; 
circuit '! 



coupling link 

Fig. 8.12 Method of coupling a tank 
circuit to an unbalanced feeder 
(from POEEJ) 


C 2 


Coaxial line 




Two- wire 

Fig. 8.13 Method of coupling a tank 
circuit to a balanced feeder 




Class B power 

0-3 kHz 



Class C 



modulated class 




Class u 


Fig. 8.14 Amplitude-modulation v.h.f. transmitter 


Sound broadcast transmitters usually employ a Class C 
biased output stage but communication transmitters, handling 
i.s.b./s.s.b. signals, use an output stage that is operated under 
Class B conditions and Fig. 8.10 shows a typical circuit. The 
circuit is tuned to the wanted frequency in the band 4-27.5 
MHz by the 77- -type network consisting of C 1; C 2 and L x . 
Unwanted second harmonics of the selected frequency are 
suppressed by the series-tuned circuit C 3 -L 3 which provides a 
low-resistance path to earth at its resonant frequency. Op- 
timum coupling to the 50 ft coaxial feeder is obtained by 
suitable adjustment of the value of inductor L 2 . All the 
variable components are motor-driven and automatically ad- 
justed when the operating frequency of the transmitter is to be 

Two other methods of coupling an output stage to a feeder 
are shown in Figs. 8.11 and 8.12. Fig. 8.11 shows how a Class 
B push-pull output stage would be coupled to a 600 ft twin 
feeder. The 600 ft impedance of the feeder is changed to the 
load impedance value required by the valves by the settings of 
the tapping points on inductor L 4 . The coupling between the 
output stage and the feeder is optimized by adjustment of the 
mutual inductance coupling between L t and L 2 and between 
L 3 and L 4 . The coupling arrangement is tuned to the required 
frequency by means of capacitors Q and C 2 . L 5 and C 3 are 
power supply decoupling components. 

Fig. 8.12 shows how an anode tuned circuit could be con- 
nected to an unbalanced coaxial feeder. The components of 
the coupling network have similar functions to those shown in 
Fig. 8.11. Coupling an output tuned circuit to a balanced twin 
feeder can be achieved in a simpler manner as shown by Fig. 
8.13. The secondary winding of the output transformer is 
centre-tapped to ensure that both conductors are at the same 
potential relative to earth. 

V.H.F. Mobile Transmitters 

The output power of most v.h.f. transmitters is only a few tens 
of watts and so completely solid state equipments can be 
designed. The block schematic diagram of a v.h.f. amplitude- 
modulated transmitter is shown in Fig. 8.14. The voltage 
generated by the microphone is amplified and then band- 
limited by the 3 kHz cut-off low-pass filter. The band-limited 
signal is amplified to the power level necessary for it to 
collector-modulate the driver and output stages of the trans- 
mitter. Although not shown in the figure, a transmitter of this 
type often has the facility for switching different crystal oscil- 
lators into circuit to permit operation at different frequencies. 
The carrier frequency can be generated directly at frequencies 


up to about 150 MHz or so using an overtone mode of the 
crystal. However, overtone crystal operation tends to be more 
expensive and of poorer frequency stability than the use of a 
lower-frequency crystal oscillator followed by one or more 
frequency multipliers. Mobile v.h.f. channels are positioned 
very close to one another in the frequency spectrum and it is 
important that a transmitter radiates little, if any, power at 
other frequencies. To ensure the adequate suppression of 
spurious frequencies an aerial filter is connected between the 
output stage of the transmitter and the aerial. 

The frequency at which a radio transmitter operates must be 
maintained constant to within internationally agreed limits to 
avoid interference with adjacent (in frequency) channels. In 
the case of s.s.b. and i.s.b. systems, the suppressed carrier must 
be re-inserted at the receiver with the correct frequency. This 
requirement will clearly be made harder if the carrier fre- 
quency at the transmitter is not constant. The oscillator from 
which the transmitter carrier frequency is derived must be of 
stable frequency, both short- and long-term. If the operating 
frequency of a transmitter is frequently changed, a variable- 
frequency oscillator of some kind must be fitted but it will then 
be difficult to achieve the desired frequency stability. 

The highest frequency stability is obtained with a crystal 
oscillator. At frequencies near the higher end of the h.f . band it 
is customary to employ a crystal oscillator operating at a low 
frequency and then to use one or more stages of frequency 
multiplication to obtain the wanted transmitted frequency. A 
crystal oscillator is a fixed-frequency circuit, and if a transmit- 
ter is to operate at different frequencies it will be necessary to 
switch different crystals into circuit. Many modern transmitters 
use a technique known as frequency synthesis to derive all the 
necessary frequencies. Typically, the frequency stability of a 
high-frequency transmitter is ±1 part in 10 6 , i.e. ±lHz if the 
carrier frequency is 10 MHz. 

Frequency Synthesis 

A frequency synthesizer is an equipment which derives a large 
number of discrete frequencies, singly or simultaneously, from 
an accurate high-stability crystal oscillator source. Each of the 
derived frequencies has the accuracy and stability of the 
source. A synthesizer may cover a wide frequency band, for 
example any frequency at 100 Hz increments between 4 MHz 
and 10 MHz. The use of a frequency synthesizer in h.f. com- 
munication transmitters has already been mentioned; many 
radio receivers also use frequency synthesis and this is 
mentioned in the following chapter. In most equipments the 
wanted frequency is selected by means of a number of decade 
switches but in the latest circuits digital control is used. 


There are two main methods available for the operation of a 
synthesizer generally known as the direct and indirect 
methods. With the DIRECT METHOD a required output 
frequency is obtained by a process of frequency multiplication, 
mixing and filtering. The stability and accuracy of the output 
frequency is set by the reference (crystal oscillator) source but 
the method has two disadvantages which have led to its 
unpopularity for use in modern systems. These disadvantages 
are that (a) the mixing process generates spurious frequencies, 
(b) a number of relatively costly filters are needed. 

Most modern equipments use the INDIRECT METHOD of 
frequency synthesis. With this method the required output 
frequency is derived from a voltage-controlled oscillator whose 
accuracy is maintained by phase-locking the oscillator to a 

Fig. 8.15 


Indirect frequency synth- 




^ Output 









standard frequency. The principle of an indirect frequency 
synthesizer is illustrated by Fig. 8.15. The phase detector is a 
circuit which, when voltages at the same frequency are applied 
to its two input terminals, produces a direct output voltage 
whose magnitude and polarity is proportional to the phase 
difference between the two input voltages. The direct output 
voltage is applied to a voltage-variable reactance (e.g. a varac- 
tor diode) which is connected as a part of the frequency- 
determining circuit of the oscillator. The effective capacitance 
of the reactance circuit is varied by the direct control voltage 
in the direction necessary to reduce the phase error of the 
voltage-controlled oscillator. 

Any tendency for the voltage-controlled oscillator to change 
frequency is opposed by the phase-control loop. As the fre- 
quency starts to drift, a control voltage is generated by the 
phase detector which changes the reactance in the direction 
necessary to correct the frequency drift. The control voltage 
must be free from alternating components, produced by noise 
or distortion, otherwise the output frequency will not be 
stable. This is the reason for the inclusion of the low-pass filter 
in the loop. 

There are various methods by which the output of the 
voltage-controlled oscillator can be used to derive all the 
wanted frequencies. One possible arrangement is shown by 






4-10 MHz 


Fig. 8.16 Frequency synthesizer 


4.4-11 MHz 

1 kHz 


1 kHz 

-o Output frequencies 




' '0.4-1 MHz 

Fig. 8.16. The output of a highly stable crystal oscillator is fed 
into a frequency-multiplication circuit which can produce an 
output frequency at any integral number of megahertz be- 
tween 4 and 10. The selected frequency is mixed with the 
output of the voltage-controlled oscillator and the sum fre- 
quency is selected. The voltage-controlled frequency can be 
set to any frequency in the range 0.4-1 MHz. and is main- 
tained accurately at this frequency by the phase-locked loop. 
The outputs of the crystal oscillator and the voltage-controlled 
oscillator are both divided down to 1000 Hz and applied to the 
phase detector. 

Another version of a frequency synthesis equipment is 
shown in Fig. 8.17. Any frequency in the band 4-8 MHz is 
made available by generating five different frequencies f x , f 2 , 
etc. and combining them by repeated mixing and filtering. 
Each of the five frequencies is produced by the phase lock 
circuit of Fig. 8.17b which shows the frequencies used for the 
f 3 decade (10-100 kHz). The crystal oscillator can operate at 
any one of ten frequencies in the band 3.555 to 3.645 MHz by 
switching different crystals into circuit. 

Frequency-modulation Transmitters 

Frequency modulation is used for sound broadcasting in the 
v.h.f. band, for v.h.f. and u.h.f. mobile systems, and for wide- 
band s.h.f. radio-relay systems. Radio-relay transmitters are 
covered in Chapter 11. 

The block schematic diagram of an f.m. sound broadcast 
transmitter is shown in Fig. 8.18. The modulating signal is 
applied to the input terminals of a varactor-diode modulated 
L-C oscillator to frequency-modulate the carrier. The 
frequency-modulated output waveform is then amplitude- 
limited to remove any amplitude modulation introduced by the 
modulator, before it is multiplied and amplified to the 
specified output power and frequency. Typical figures are 



U f-> 

f^f 2 +f 3 


fi+f 2 +f 3 +f 4 f^f 2 +f 3 + U + h 



3.555-3.645 MHz 
Crystal oscillator 


Fig. 8.17 Frequency synthesizer 
used in a h.f. communication trans- 
mitter: (a) basic arrangement, (fa) 
10 kHz component generator (From 
Post Office Electrical Engineers' 










5 kHz 



100 kc/s 

20 kHz 






frequency p 



Class B or C 
tuned power 

B Aerial 

Fig. 8.18 Frequency-modulation 
v.h.f. transmitter 

Fig. 8.19 Frequency-modulation 
v.h.f. transmitter using indirect mod- 

91.3 MHz and 10 kW. The centre (unmodulated) carrier fre- 
quency radiated by the transmitter must be very stable, 
typically ±1 kHz per year, and since the inherent frequency 
stability of an L-C oscillator is inadequate automatic fre- 
quency control must be applied. 

Many transmitters, particularly those used in narrowband 
mobile systems, use the indirect method of frequency modulat- 
ing a carrier because of the improved frequency stability then 
provided. The block diagram of a typical narrowband f.m. 
communication transmitter is given by Fig. 8.19. The mic- 
rophone output voltage is amplified, integrated, amplitude- 

Amplifier correction Limitei 


Phase Frequency 
modulator multiplication 


Class C ™" 
Frequency tuned 
multiplication amplifier 






limited and finally band-limited before used to frequency- 
modulate the carrier voltage generated by the crystal oscil- 
lator. The frequency deviation of the modulated wave is 
always small, often less than 100 Hz, and must be increased by 
several stages of frequency multiplication before it reaches the 
final Class C output power amplifier stage. 

If a carrier at frequency f c is frequency modulated with a 
frequency deviation of kf d and is then passed into a frequency 
doubler, the output voltage of the doubler will be at a fre- 
quency of 2(/ c ±f d ) or 2f c +2kf d . This means that the deviation 
ratio of the wave has been doubled. Thus the use of frequency 
multiplication will increase both the carrier frequency and the 
deviation ratio by the same ratio. 

Use of Frequency Mixing 

The process of mixing produces the sum and the difference of 
the frequencies of two signals. Suppose a frequency-modulated 
wave is mixed with a frequency / ; the output of the mixer 
then contains components at frequencies of / ±(/ c ±fc/ d ) and 
either the sum or the difference frequency can be selected. It 
can be seen that the selected output frequency is 

either (f + f c )±kf d or (f -f c )±kf d 

but the frequency deviation kf d and hence the deviation ratio 
is unchanged. To obtain a particular value of carrier frequency 

nf c ± nkf d (n1 c + mf c ) ± nkf d 

f. + kf* 



Class C 
tuned power 















(nf c + mf c ) ± nkf d 





Fig. 8.20 Method of obtaining particular values of carrier fre- 
quency and deviation ratio 

together with a particular deviation ratio, it may well be 
necessary to use a suitable combination of both frequency 
changing and mixing as shown by Fig. 8.20. 

High Voltage Components and Precautions 

The thermionic valves and other components used in a high- 
power stage of a radio transmitter must be able to withstand a 


voltage of several thousands of volts and so special high- 
voltage types must be used. The maximum permissible voltage 
which can be safely applied across a resistor is limited because 
of the danger of a dielectric breakdown. Any such breakdown 
appears in the form of sparking. Another factor which must be 
considered is the power rating of a resistor. If this is exceeded, 
excessive heat will be dissipated within the component and its 
resistance will change, possibly by a significant amount. 
Ceramic carbon resistors are probably the best type to use 
since they have voltage ratings of 20 kV or more. Similarly the 
voltage rating of a capacitor is determined by the need to 
ensure that the dielectric between the plates does not break 

The design of a high-voltage inductor is constrained by the 
need to avoid the insulation (very likely air) between adjacent 
turns breaking down because of the electric field across it. This 
means that the turns must be spaced well apart from one 
another and probably be self-supporting. Also, the inductor in 
a series-feed circuit will have a current of several amperes 
flowing in it and must be manufactured using a conductor of 
large cross-sectional area. Often the power dissipated within a 
high-voltage inductor is so large that the component must be 
cooled by blowing cool air around it. In all cases high-voltage 
components must not be allowed to become too hot and the 
equipment design must ensure adequate ventilation. 

The valve in the output stage, and perhaps the penultimate 
stage also, of a high-power transmitter may be called upon to 
dissipate several kilowatts of power at its anode, and in the 
case of a tetrode at its screen grid also. The anode will become 
extremely hot because of the power dissipated at it and this 
heat must be removed to keep the temperature of the anode 
within acceptable limits. When the anode dissipation is not 
very large, say less than 1.5 kW, sufficient heat can be re- 
moved by fabricating the copper anode as an integral part of 
the valve's envelope and relying on direct radiation. When the 
anode dissipation is larger than 1 .5 kW the rate of removal of 
heat must be speeded up by passing cooling air, or water, 
around the anode. In modern transmitters, cooling of the anode 
is achieved using a vaporization technique. The basic idea of a 
water vapour cooling system is that cooling water is converted 
into steam by the heat of the anode, this steam is removed and 
condensed back into water, and then the water is re-circulated 
past the anode. 

Because of the very high voltages present at various points 
in a high-power transmitter, various precautions must be taken 
to ensure the safety of the persons required to carry out tests 
or repairs on the equipment. All high-voltage points in the 
transmitter are mounted inside interlocking cabinets or cages. 
Entry within a cage can only be made by following a proce- 


dure which ensures that the panel giving access to the interior 
of the equipment can only be opened after the high-voltage 
has been removed. This is generally arranged by feeding in the 
power supplies via an isolating unit that is interlocked with an 
earthing switch. The keys necessary to unlock the panel can 
only be obtained after the isolating unit has been operated to 
disconnect the power supply and earth the equipment. Usu- 
ally, different parts of the transmitter are housed inside differ- 
ent cabinets, for example one cabinet might contain the power 
supply circuitry and another the r.f . power output stage. When 
work on the equipment is completed it is necessary to follow 
the reverse procedure, i.e. all entry panels must be replaced 
and locked and the keys restored before the power supplies 
can be switched on again. 


8.1. (a) Describe, with the aid of a block diagram, the drive and r.f. 
stages of a high-power independent-sideband h.f. transmitter. 
How is crosstalk between sidebands minimized? (b) Compare 
and contrast independent-sideband operation with (i) double 
sideband, (ii) single sideband operation. (C & G) 

8.2. (a) Briefly discuss the considerations which enter into the 
design of the output stage of an h.f. transmitter, (b) Give two 
reasons why each aerial at an h.f. transmitting station is not 
permanently associated with a transmitter, (c) Explain briefly 
why a transmitter must be matched to an aerial feeder. 

(C & G) 

8.3. Fig. 8.21 is the block diagram of a marine f.m. transmitter, (a) 
State the purpose of the limiter in the microphone amplifier, (b) 
What is the purpose of the audio-frequency corrector? (c) How 
is the stability of the frequency generator maintained for differ- 
ent channels? (d) Explain briefly the function of the modulator, 
(e) If the frequency generator has an 8.7 MHz output what is 
the frequency band required for speech signals? (/) State briefly 
how an amplifier may be used as a frequency multiplier, (g) If 
the power amplifier uses a self-biased valve operated in Class 
C, what would be the effect on its anode current of the failure 
of a previous stage? (h) Why is a vertical aerial used for 
transmission? (C & G) 




amp. & 











Hg. 8.21 





8.4. Draw the block diagram of the drive and r.f. stages of a 
high-power short-wave independent-sideband transmitter. (b) 
Describe briefly the operation of this transmitter, describing 
how the independent sidebands are combined, (c) Draw the 
spectrum of the signal at three representative points in your 
diagram taking care to distinguish between the sidebands in 
each. (C & G) 

8.5. (a) Draw the block diagram of a medium-frequency broadcast 
transmitter, (b) What is the class of operation of each stage? (c) 
How is frequency control obtained? (d) For such a transmitter, 
what is a typical (i) frequency range, (ii) frequency stability (iii) 
power delivered to the aerial? (C & G) 

8.6. (a) What do you understand by the terms (i) high-level modula- 
tion, (ii) low-level modulation? Illustrate your answers with 
block diagrams of amplitude-modulation transmitters, (b) What 
class of operation is usual for the final stage amplifiers for each 
of these types of transmitter? (c) What do the following ab- 
breviations stand for when used in conjunction with amplitude- 
modulation transmissions: (i) s.s.b., (ii) d.s.b., (iii) d.s.b.s.c, (iv) 
i.s.b.? (d) Using sketches of a sinusoidal modulating signal and 
a sinusoidal carrier signal illustrate the waveform of a mod- 
ulated signal using (i) d.s.b., (ii) d.s.b.s.c, (iii) s.s.b. types of 
modulation. (C & G) 

8.7. (a) Draw the block diagram of an amplitude-modulated high- 
power telephony transmitter for a point-to-point system cover- 
ing the 4 MHz to 27.5 MHz band, (b) Describe briefly the 
operation of this transmitter, explaining how rapid frequency 
changing is facilitated, (c) Why is regular frequency changing 
necessary and about how long does it take in a modern trans- 
mitter? (d) Using a sketch, show how, in a modern system, a 
transmitter of this type is switched from one aerial to another. 


8.8. With the aid of a circuit diagram explain the operation of a 
v.h.f. telephony transmitter using high-power modulation. 


8.9. (a) Using a fully labelled block diagram, explain the principle 
of operation of the Armstrong method of obtaining wideband ' 
frequency modulation, (b) In a particular Armstrong modulator 
the side-frequencies produced by a 3 kHz sinusoidal modulat- 
ing signal are each 6 dB down on the amplitude of the 30 kHz 
sub-carrier. If the final carrier is radiated at a nominal 90 MHz, 
calculate the frequency deviation of this transmission. 


8.10. Discuss the advantages and disadvantages of the following as 
the drive unit for a transmitter: (a) variable-frequency oscil- 
lator, (b) crystal-controlled oscillator, (c) frequency synthesizer. 


8.11. (a) What is meant by the terms (i) deviation ratio, (ii) modula- 
tion index as applied to frequency modulation transmissions? 
(b) With aid of a circuit diagram show how, by means of a 
varactor diode, a 5 MHz oscillator could be frequency mod- 
ulated by a 2 kHz audio signal, (c) The output of the oscillator 
is converted to 90 MHz by (i) frequency multiplication, (ii) 
mixing with output of an 85 MHz oscillator. Assuming the 
deviation produced by the varactor diode to be 3 kHz, deduce 
the final deviation in each case. (C & G) 


8.12. (a) What is meant by the term "frequency synthesis"? (b) Use 
a block diagram to illustrate how frequency synthesis is used in 
a modern radio telephony transmitter, (c) In a certain synth- 
esizer a 2(n — 2) divider chain output is equal to a 500 kHz 
reference frequency. If the input to the dividers is the difference 
between ten times the reference frequency and the synthesized 
frequency, what value of n should be selected to derive a 
158 kHz output? (C & G) 

8.13. (a) Using circuit diagrams to illustrate your answers show how 
(i) a telephony transmitter with a Class B push-pull output stage 
would be coupled to a 600 fl transmission line, (ii) a transmitter 
output tank circuit would be connected to a coaxial line aerial 
feeder. Show how matching and tuning are facilitated, (b) 
Briefly explain how a high-power transmitting valve is pro- 
tected in the event of a feeder or aerial failure. (C & G) 

Short Exercises 

8.14. Why is there a need of high-efficiency in the final stage of a 
radio transmitter? 

8.15. What is the function of a tuned power amplifier in a radio 

8.16. (a) Why does an h.f. communication transmitter need to 
change frequency fairly often? (b) Why does an h.f. broadcast 
transmitter remain at the same frequency? 

8.17. Why is frequency stability necessary in a radio transmitter? 
How is it obtained in (i) an h.f. communications transmitter, (ii) 
a v. h.f. f.m. communication transmitter? 

8.18. List the requirements of the output stage of a high-frequency 
radio transmitter. 

8.19. Refer to the block diagram of a v.h.f. a.m. transmitter given in 
Fig. 8.14 and answer the following questions, (a) Why is the 
modulating signal band-limited? (b) Why are two stages of r.f. 
power gain collector modulated? (c) How is the transmitted 
frequency changed? (d) Why is an aerial filter fitted? 

8.20. What is meant by frequency synthesis and why is it used in 
modern h.f. transmitters? 

8.21. Draw the block diagram of an i.s.b. drive unit and a low-level 
main transmitter and show how the transmitter can be switched 
to operate with one of several aerials. 

8.22. (a) Why is a limiter often used in an f.m. transmitter? (b) Why 
is a phase modulator often used? 


Radio Receivers 


The functions of a radio receiver are to select the wanted 
signal from all those signals picked up by the aerial, to extract 
the information which has been modulated on to the wanted 
signal, and then to amplify the signal to the level necessary to 
operate the loudspeaker or other receiving device. A radio 
receiver may be designed to receive sound broadcast signals 
using d.s.b. amplitude modulation or using frequency modula- 
tion; for use with land, maritime, or aero-mobile systems using 
amplitude or frequency modulation; or for use in a multi- 
channel point-to-point radio link. For reasons discussed 
elsewhere [RSII] radio receivers are of the superheterodyne 

The Superheterodyne Radio Receiver 

In a superheterodyne radio receiver the wanted signal frequency 
is converted into a constant frequency — known as the inter- 
mediate frequency — at which most of the gain and the selectiv- 
ity of the receiver is provided. 

The basic block diagram of a superheterodyne radio receiver 
is shown in Fig. 9.1. The, wanted signal, at frequency X is 
passed, together with many other unwanted frequencies, by 


Wanted signal f s 
plus other frequencies 


± f s pl 


us other 




















Fig. 9.1 The superheterodyne radio 



the radiQ-irequency-stage_taihejiiixei ^or frequency changer). 

The r.f^stage-is not provided to select the wanted signal but 

chiefly to prevent certain particularly troublesome frequencies 

, ^ x_. reaching the mixer stage. In the mixer stage the input frequen- 

^ <t? cies are combined with the output of the local oscillator, at a 

o frequency f„, to generate components at a large number of new 

frequencies. Amongst the newly generated frequencies are 

components at the sum and the difference of the wanted signal 

and the local oscillator frequencies, i.e. at f ±f s . 

The difference frequency f —f s is known as the INTER- 
MEDIATE FREQUENCY and is selected by the inter- 
mediate frequency (i.f.) amplifier. The intermediate frequency 
is a fixed frequency and this means that, 'when a receiver is 
tuned to receive a signal at a particular frequency, the local 
oscillator frequency is adjusted so that the correct difference 
frequency is obtained. The amplified output of the i.f. amp- 
lifier is applied to the detector stage and it is here that the 
information contained in the modulated signal is recovered. 
The detected signal is amplified to the .required power level by 
the audio-frequency amplifier and is then fed to the loud- 
speaker, [telephone or other output device. 

A number of differences exist between receivers designed 
for the reception of amplitude- and frequency-modulated 
transmissions and i.s.b./s.s.b. radio-telephony signals. The main 
differences are as follows: 

(a) The r.f. stage in an a.m. broadcast receiver may not 
include amplification whereas the other types of receiver 
always provide gain. 

(b) The bandwidths of the r.f. and the i.f. stages are consid- 
erably different; often h.f. communication receivers have 
a variable bandwidth facility since they may be designed 
to cater for a number of different kinds of signal. 

(c) Mainly because of the different bandwidths required, 
different intermediate frequencies are used. 

(d) Different types of detector circuit are used. 

Most frequency modulation broadcast receivers are also 
capable of the reception of amplitude-modulation signals; 
when discrete components are used the arrangement shown in 
Fig. 9.2 is common; the switches are shown in their f.m. 
positions. The wanted f.m. signal is converted to the inter- 
mediate frequency by the F.M. TUNER and then delivered to 
the first common stage of the i.f. amplifier. This stage has the 
dual function of first i.f. amplifier for f.m. signals and mixer 
stage for a.m. signals. The wanted f.m. signal is selected by the 
first i.f. amplifier, amplified, and then passed on to the next 
stage of i.f. amplification. The amplified f.m. signal is then 
applied to the detector where its information content is ex- 



F.M. tuner 








F.M./I.F. / 
1st / 
amp / 

/ A.M. 
/ mixer 

F.M./I.F. / 
2nd / 
amp / 

/ 1st amp 

F.M./I.F. / 
3rd / 
amp x' 

x' 2nd amp 



/S 2 





Fig. 9.2 F.M./A.M. superheterodyne radio receiver 

tracted and then passed to the a.f. amplifier. When amplitude 
modulation signals are to be received, all the switches shown 
are operated and the first i.f. stage then acts as the a.m. mixer. 
The amplitude-modulated i.f. signal is selected by the second 
i.f. amplifier stage, which now acts as the first i.f. amplifier, and 
is then applied to the a.m. detector. The use of dual function 
stages is common since it results in a considerable reduction in 
the number of components needed. 

Integrated circuits are increasingly employed in radio receiv- 
ers, and Figs. 9.3 and 9.4 show two examples of modern 
practice. Fig. 9.3 shows the block diagram of an a.m. receiver; 
one i.e. performs the functions of the mixer, the i.f. amplifier, 
the detector, and the audio pre-amplifier; the other i.e. acts as 
the a.f. power amplifier. Provided externally to these inte- 
grated circuits are the components forming the r.f. stage and all 
the necessary inductors, capacitors and resistors for the other 
stages which cannot be formed within the i.e. package. The 

Fig. 9.3 Superheterodyne radio re- 
ceiver using integrated circuits 



(mixer, i.f. 
amp, detector, 
a.f. pre-amp) 

I.C 2 

(a.f. power 






Fig. 9.4 F.M./A.M. superhetero- 
dyne radio receiver using inte- 
grated circuits. 




r.f. stage 


(i.f. amp and 



(Mixer, i.f. amp 
and detector) 



(a.f. amp) 


block diagram of an f.m./a.m. receiver which uses integrated 
circuits is given in Fig. 9.4. The a.m. and f .m. sections of the 
receiver are completely separate up to the outputs of the two 
detector stages. The f.m. signal is amplified and frequency 
changed by the (non-integrated) f.m. tuner (often in module 
form), and is then passed on to an i.e. which performs the 
functions of both the i.f. amplifier and the f.m. detector; the 
selectivity of the i.f. amplifier is determined by an external 
inductor/capacitor network. The a.m. signal is received by a 
normal r.f. stage and is then fed to an integrated circuit which 
acts as the mixer, the i.f. amplifier and the a.m. detector. The 
audio-frequency outputs of the two detectors are connected, 
via a switch, to the common audio-frequency amplifier. The 
selectivity of the a.m. i.f. amplifier is determined by a ceramic 

Choice of Local Oscillator Frequency 

The intermediate frequency of a superheterodyne radio re- 
ceiver is the difference between the wanted signal frequency 
and the local oscillator frequency. Two possibilities exist: the 
local oscillator frequency can be higher than the signal fre- 
quency, or vice versa. 

Consider a receiver with an intermediate frequency of 
470 kHz that is tunable over the band from 525 kHz to 
1605 kHz. If the frequency of the local oscillator is higher than 
the wanted signal frequency the oscillator must be tunable 

(525 +470) = 995 kHz to (1605+470) = 2075 kHz 

a frequency ratio of 2075/995, or 2085 : 1. Such a frequency 
ratio would require the use of a variable capacitor having a 
ratio maximum-capacitance/minimum-capacitance of (2.085) 2 , 
or 4-35 : 1. Such a capacitance ratio is easily obtained. 


The alternative is to make the signal frequency higher than 
the local oscillator frequency. The oscillator frequency must 
then be variable from 

(525-470) = 55 kHz to (1605-470) = 1135 kHz 

This is a frequency ratio of 1135/55, or 20-64: 1 and requires 
a capacitance ratio of (20-64) 2 , or 425-9:1. Such a large 
capacitance ratio could not be obtained with a single variable 
capacitor and so tuning would not be as easy or cheap to 

It is therefore usual to make the local oscillator frequency 
higher than the wanted signal frequency, i.e. 

fo = fs+fi (9.1) 

The sum frequency component of the mixer output is not 
chosen for the intermediate frequency because it would mean 
that the latter would have to be greater than the highest 
frequency in the tuning range of the receiver. The various 
factors leading to the choice of intermediate frequency will be 
discussed later; here it will suffice to say that use of the sum 
frequency would prevent the use of the optimum intermediate 

Image Channel Interference 

No matter what frequency a superheterodyne receiver is tuned 
to, there is always another frequency that will also produce the 
intermediate frequency. This other frequency is known as the 
IMAGE FREQUENCY. The image signal has a frequency f im 
such that the difference between it and the local oscillator 
frequency is equal to the intermediate frequency, /;, i.e. 

ti = Jim ~ ]0 

Substituting for f from equation (9.1), 



f im =fs+2f i (9.2) 

The image signal is thus separated from the wanted signal by 
twice the intermediate frequency. The image signal must be 
prevented from reaching the mixer or it will produce an 
interference signal which, since it is at the intermediate fre- 
quency, cannot be eliminated by the selectivity of the i.f. 
amplifier. The r.f. stage must include a resonant circuit with 
sufficient selectivity to reject the image signal when tuned to 
the wanted signal frequency. Tuning is necessary because the 
wanted signal frequency, and hence the image signal fre- 


quency, will vary. It is not difficult to obtain a resonant circuit 
with good enough selectivity to accept the wanted signal and 
reject the image signal when their separation is an appreciable 
fraction of the wanted signal frequency. As the signal fre- 
quency is increased, the fractional frequency separation be- 
comes smaller and the image rejection less efficient. 

Any vestige of the image signal reaching the mixer will 
produce a signal appearing as crosstalk at the output of the 
receiver. If a signal at a few kilohertz away from the image 
signal should reach the mixer, the two i.f. signals produced 
would beat together to produce a whistle at the output of the 

The image response ratio is the ratio, in decibels, of the 
voltages at the wanted signal and image signal frequencies 
necessary at the receiver input terminals to produce the same 
audio output. 


(A) A superheterodyne radio receiver has an intermediate frequency 
of 470 kHz and is tuned to 1065 kHz. Calculate (a) the frequency of 
the local oscillator, and (b) the frequency of the image signal. 


From equation (9.1) 

/ = 1065 + 470 = 1535 kHz (Ans.) 

and from equation (9.2) 

f im = 1065 + 940 = 2005 kHz (Ans.) 

(B) A superheterodyne radio receiver has an intermediate frequency 
of 10.7 MHz and is tuned to 97.3 MHz. Calculate (a) the frequency 
of the local oscillator and (b) the image channel frequency. 


From equation (9.1) 

/„ = 97.3 + 10.7 = 108.0 MHz (Ans.) 

and from equation (9.2) 

f tm = 97.3 + 21.4= 118.7 MHz (Ans.) 


I.F. Breakthrough 

If a signal at the intermediate frequency is picked up by an 
aerial and allowed to reach the mixer, it will reach the i.f. 
amplifier and interfere with the wanted signal. Such a signal 
must therefore be suppressed in the r.f. stage by an i. f. trap. 
The i.f. trap consists of either a parallel-resonant circuit, tuned 
to the intermediate frequency, connected in series with the 
aerial lead, or a series-resonant circuit, also tuned to the 
intermediate frequency, connected between the aerial lead and 
earth. In the first circuit the i.f. trap has a high impedance and 
blocks the passage of the unwanted i.f. signal; in the second 
circuit the i.f. trap has a low impedance and shunts the 
unwanted signal to earth. 


A superheterodyne radio receiver has an intermediate frequency of 
465 kHz and is tuned to receive an unmodulated carrier at 1200 kHz. 
Calculate the frequency of the audio output signal if present at the 
mixer input there are also (a) a 1208 kHz, and (b) a 462 kHz 
sinusoidal signal. 


(a) The local oscillator frequency is 465 + 1200= 1665 kHz, and 
hence the 1208 kHz signal produces a difference frequency output 
from the mixer of 1665 - 1208 = 457 kHz. If the i.f. bandwidth is only 
9 kHz centred on 465 kHz, the 457 kHz signal will be rejected. 

(b) The 462 kHz signal will appear at the mixer output and will be 
passed by the i.f. amplifier and will beat with the 465 kHz signal to 
produce a 3 kHz tone at the receiver output. 

Other Sources of Interference 

A superheterodyne receiver is also exposed to a number of 
other sources of interference. Co-channel interference is due to 
another signal at the same frequency and cannot be eliminated 
by the receiver itself. When it occurs it is the result of unusual 
propagation conditions making it possible for transmissions 
from a distant (geographically) station to be picked up by the 
aerial. Harmonics of the local oscillator frequency may com- 
bine with unwanted stations or with harmonics produced by 
the mixer to produce various difference frequency compo- 
nents, some of which may fall within the passband of the i.f. 
amplifier. It is also possible for two r.f. signals arriving at the 
input to the mixer to beat together and produce a component 
at the intermediate frequency. 


The transfer and mutual characteristics of a bipolar or a 
field-effect transistor exhibit some non-linearity and as a result 
the output waveform will contain components at frequencies 
which were not present at the input. If, for example, the input 
signal contains components at frequencies f x and f 2 , the output 
may contain components at frequencies /i±/ 2 » 2/i±/ 2 , 2/ 2 ±/i, 
etc. These new frequencies are known as intermodulation 
products. Intermodulation can take place in both the r.f. amp- 
lifier and the mixer if the input signal level is so high that the 
active device is operated non-linearly. If two unwanted strong 
signals, separated in frequency by the intermediate frequency, 
or near to it, are present at the r.f. amplifier or mixer stages, they 
will produce an interfering component that will not be rejected 
by the i.f. amplifier. 

One example of intermodulation which particularly affects 
v.h.f./f .m. receivers is known as half i.f. interference. Consider 
two signals at frequencies / and /+§/# to be present at the r.f. 
stage and to produce a voltage at their difference frequency. 
The second harmonic of this component is 2[/— (/+|/ jf )] which 
is equal to the intermediate frequency of the receiver. 

Intermodulation interference can be reduced by operating 
the r.f. stage as linearly as possible and if possible rejecting 
one of the input voltages generating the interference. 

Local Oscillator Radiation 

The local oscillator operates at a radio frequency and may well 
radiate either directly or by coupling to the aerial. Direct 
radiation is limited by screening the oscillator. Radiation from 
the aerial is reduced by using an r.f. amplifier to prevent the 
oscillator voltage reaching the aerial. Radiation of the local 
oscillator frequency does not have a detrimental effect on the 
receiver in which it originates but is a source of interference to 
other nearby receivers. 


Cross-modulation is the transfer of the amplitude modulation 
of an unwanted carrier onto the wanted carrier and is always 
the result of non-linearity in the mutual characteristic of the 
r.f. amplifier or of the mixer. If the amplitude of the input 
signal is small, or the mutual characteristic is essentially square 
law, cross-modulation will not occur. The unwanted signal may 
lie well outside the passband of the i.f. amplifier but, once 
cross-modulation has occurred, it is not possible to remove the 
unwanted modulation from the wanted carrier. 

Cross-modulation is only present as long as the unwanted 
carrier producing the effect exists at the aerial, and it can be 
minimized by linear operation of the r.f. stage and by increas- 


ing the selectivity of the r.f. stage to reduce the number of 
large-amplitude signals entering the receiver. It is also helpful 
to avoid applying a.g.c. to the r.f. stage and, if large amplitude 
signals are expected, to use a switchable aerial attenuator to 
reduce the signal level and avoid overload with its consequent 
non-linearity. Cross-modulation does not occur in a 
frequency-modulation receiver because the unwanted amp- 
litude variations will be removed by the limiter stage. 


Blocking is an effect in which the gain of one or more stages in 
a radio receiver is reduced by an interfering signal of sufficient 
strength to overload the stage, or to excessively operate the 
a.g.c. system of the receiver. The practical result of blocking is 
that the wanted signal output level falls every time the inter- 
fering signal is received. 

Fig. 9.5 Selectivity characteristics 
of radio receivers 


The SELECTIVITY of a radio receiver is its ability to discrimi- 
nate between the wanted signal and all the other signals picked 
up by the aerial, particularly the adjacent-channel signals. The 
selectivity of a receiver is usually quoted by means of a graph 
showing the output of the receiver, in dB relative to the 
maximum output, plotted against the number of kHz off-tune 
or by quoting some points on this graph. For example, the 
selectivity of an h.f . receiver may be quoted as -6 dB at 3 kHz 
bandwidth and -60 dB at 12 kHz bandwidth. Fig. 9.5 shows 
typical selectivity curves for a.m. broadcast, f.m. broadcast, 
and h.f. s.s.b. communication receivers. Clearly, there are 
large differences between the 3dB bandwidths of the three 
receivers; the a.m. broadcast receiver has a 3 dB bandwidth of 

f.m. broadcast receiver 

Signal frequency 

Frequency (kHz off-tune) 


about 9 kHz, the s.s.b. receiver approximately 3 kHz, but the 
f .m. broadcast receiver's bandwidth is about 200 kHz. 

The adjacent channel selectivity of a radio receiver is mainly 
determined by the gain/frequency characteristic of the i.f. 

The ADJACENT CHANNEL RATIO is the ratio, in dB, of 
the input voltages at the wanted and the adjacent channel 
frequencies necessary for the adjacent channel to produce an 
output power 30 dB smaller than the signal power. 


A superheterodyne radio receiver is tuned to a certain frequency at 
which an input signal of 15 ^ V produces an output of 50 mW. If the 
input voltage at the adjacent-channel frequency needed to produce 
—30 dB output power is 1.5 mV calculate the adjacent channel ratio. 


/l 5 x 10 _3 \ 
Adjacent channel ratio = 20 log 10 — — ——r ) = 40 dB (Ans.) 

\15xl0 6 7 

The 6 dB and the 60 dB bandwidths are often known, 
respectively, as the nose and the skirt bandwidths. The NOSE 
BANDWIDTH is the range of frequencies over which a signal 
can be received with little practical loss of strength. The 
SKIRT BANDWIDTH is the band of frequencies over which 
it is possible to receive a strong signal. The ratio of the skirt 
bandwidth to the nose bandwidth is known as the shape factor. 
Thus the h.f. s.s.b. receiver quoted earlier has a nose band- 
width of 3 kHz, a skirt bandwidth of 12 kHz, and a shape 
factor of 12 kHz/3 kHz or 4.0. 

The selectivity curves shown in Fig. 9.5 relate to a single 
input frequency and do not entirely predict the performance of 
a receiver when signals at several different frequencies are 
simultaneously received. The effective selectivity of a receiver 
when interfering signals are present is determined by the 

(a) The selectivity provided by the r.f . stage. 

(b) The ability of the r.f. stage to handle strong signals. 

(c) The adjacent-channel selectivity provided by the i.f. 

Factors (a) and (b) arise because of the possibility of spuri- 
ous frequencies at or near the intermediate frequency being 
produced by intermodulation. 


The SENSinvrrY of a radio receiver is the smallest input 
signal voltage that is required to produce a specified output 
power with a specified signal-to-noise ratio. For amplitude- 


modulation receivers, the specified output power is usually 
50 mW with a signal-to-noise ratio of 20 dB and the input 
signal modulated 30% at 1000 Hz (or 400 Hz). For an f.m. 
receiver a signal-to-noise ratio of 40 dB is required with the 
input signal modulated by a 1000 Hz signal to give 30% 
modulation. (This means that the frequency deviation pro- 
duced should be 30% of the rated system deviation, i.e. for the 
v.h.f. sound broadcast system 30% of 75 kHz is 22.5 kHz.) 

It is necessary to include signal-to-noise ratio in the defini- 
tion of sensitivity, otherwise the output power could consist 
mainly of noise and be of little use. 

The sensitivity of a radio receiver is determined by 

(a) The overall voltage gain of its individual stages. 

(b) The gain/frequency characteristic of the r.f. stage. 

(c) The noise generated by thermal agitation in its input 

This means that the sensitivity is directly related to the noise 
figure of the receiver. 

Typical figures for sensitivity are (a) a.m. broadcast receiver 
50 fiV, (b) f.m. broadcast receiver 2 /nV, and (c) s.s.b. receiver 
1 fiV. 

Noise Figure 

The output of a radio receiver must always contain some noise 
and the receiver must be designed so that the output signal-to- 
noise ratio is always at least as good as the minimum figure 
required for the system. The noise appearing at the receiver's 
output terminals originates from two sources; noise picked up 
by the aerial and noise generated within the receiver [EIII]. 
Because of the internally generated noise, the signal-to-noise 
ratio at the output terminals is always less than the input 
signal-to-noise ratio. The noise figure or factor of a radio 
receiver is a measure of the degree to which the receiver 
degrades the input signal-to-noise ratio. The NOISE FAC- 
TOR F is related to the input and output signal-to-noise ratios 
by equation (9.3): 

Input signal-to-noise ratio 
Output signal-to-noise ratio 

An ideal receiver would have no internal noise sources and 
would not degrade the input signal-to-noise ratio; hence its 
noise figure would be unity or zero dB. 



The signal-to-noise ratio at the input to a communication receiver is 
40 dB. If the receiver has a noise figure of 12 dB calculate the output 
signal-to-noise ratio. 


From equation (9.3) 

Input signal-to-noise ratio 

Output signal-to-noise ratio = — -— — 

Noise factor 

or in dB 

Output signal-to-noise ratio = 40 — 12 = 28 dB (Ans.) 

The Radio-frequency Stage 

The radio-frequency stage of a superheterodyne radio receiver 
must perform the following functions: 

(a) It must couple the aerial to the receiver in an efficient 

(b) It must suppress signals at or near the image and the 
intermediate frequencies. 

(c) At frequencies in excess of about 3 MHz it must provide 

(d) It must operate linearly to avoid the production of 

(e) It should have sufficient selectivity to minimize the 
number of frequencies appearing at the input to the 
mixer that could result in intermodulation products lying 
within the passband of the i.f. amplifier. 

At frequencies up to about 3 MHz or so, the noise picked up 
by an aerial is larger than the noise generated within the 
receiver. An r.f. amplifier will amplify the aerial noise as well 
as the signal and produce little, if any, improvement in the 
output signal-to-noise ratio. At higher frequencies the noise 
picked up by the aerial falls and the constant-level receiver 
noise becomes predominant; the use of r.f. gain will then 
improve the output signal-to-noise ratio. An r.f. amplifier also 
permits the use of two or more tuned circuits in cascade, with 
a consequent improvement in the image response ratio. 

The Mixer Stage 

The function of the mixer stage is to convert the wanted signal 
frequency into the intermediate frequency of the receiver. This 
process is carried by mixing the signal frequency with the 
output of the local oscillator and selecting the resultant differ- 
ence frequency. 


The local oscillator must be capable of tuning to any fre- 
quency in the band to which the receiver is tuned plus the 
intermediate frequency, i.e. /o = /*+./;/• The ability of a re- 
ceiver to remain tuned to a particular frequency without 
drifting depends upon the frequency stability of its local oscil- 
lator. In an a.m. broadcast receiver the demands made on the 
oscillator in terms of frequency stability are not stringent since 
the receiver is tuned by ear. High-frequency communications 
receivers need greater frequency stability mainly because the 
channel bandwidth is narrow. Receivers operating at one or 
more fixed frequencies can use a crystal oscillator, frequency 
changes involving crystal switching. When a receiver is to be 
tunable over a band of frequencies an L-C oscillator with 
automatic frequency control or a frequency synthesizer must be 

The frequency stability of an i.s.b./s.s.b. receiver should be 
good enough to ensure that the tuning of the receiver will not 
drift from its nominal value by more than about 20 Hz over a 
long period of time. This is necessary because any change in 
the local oscillator frequency will cause a corresponding shift 
in the frequency of the output signal. If, for example, the 
oscillator frequency should be 10 Hz too high, then all the 
components of the output signal will also be 10 Hz too high. If 
data and/or v.f. telegraph signals are to be received, the 
maximum permissible frequency drift is only ± 1 Hz. Gener- 
ally, the long-term frequency stability of an h.f. communica- 
tions receiver is better than 1 part in 10 7 . 

Ganging and Tracking 

When a superheterodyne radio receiver is tuned to receive a 
particular signal frequency, the resonant circuit(s) in the r.f. 
stage must be tuned to that frequency and the tuned circuit of 
the local oscillator must be tuned to a frequency equal to the 
sum of the signal and the intermediate frequencies. Clearly it 
is convenient if the tuning of these circuits can be carried out 
by a single external control. To make this possible the tuning 
capacitors are mounted on a common spindle so that they can 
be simultaneously adjusted; this practice is known as GANG- 
ING. The maintenance of the correct frequency difference (the 
intermediate frequency) between the r.f. stage and local oscil- 
lator frequencies is known as TRACKING. 

It is possible to achieve nearly perfect tracking over one 
particular waveband if the plates of the oscillator tuning 
capacitor are carefully shaped, but this practice requires a 
different capacitor for each waveband and involves design 
problems. Most radio receivers use identical tuning capacitors 
for the r.f. and oscillator circuits and modify the capacitance 
values by means of trimmer and/or padder capacitors. 


SpF = 

1 V 

40-440 pF 

Fig. 9.6 Use of a trimmer capacitor 
in the r.f. stage 

Consider a receiver designed to tune over the medium 
frequency band of 525-1605 kHz and have an intermediate 
frequency of 470 kHz. Suppose that the (identical) variable 
tuning capacitors used in the r.f. and oscillator circuits have a 
capacitance range of (maximum capacitance — minimum 
capacitance) of 400 pF. The r.f. stage must tune over the band 
525-1605 kHz; this is a frequency ratio of 1605/525 or 
3.057 : 1 and requires the tuning capacitance to provide a 
capacitance ratio of 3.057 2 : 1 or 9.346 : 1. Therefore, if the 
minimum capacitance needed is denoted by x, then 

9.346x = x+400 

x = 400/8.346 = 47.93 pF^ 48 pF 

The maximum capacitance must then be 48 + 400 = 448 pF. If 
the minimum capacitance of the variable capacitor plus the 
inevitable stray capacitances is not equal to 48 pF, a TRIM- 
MER capacitance must be connected in parallel with the 
tuning capacitance. For example, if the minimum tuning 
capacitance plus stray capacitances adds up to 40 pF, an 8 pF 
trimmer will be required (see Fig. 9.6). The inductance L x 
required to tune the r.f. stage to the wanted signal frequency 
can be calculated using the expression f = l/2irV(LC), re- 
membering that the minimum capacitance corresponds to the 
maximum frequency and vice versa. Thus 

L 1 = l/(4-n- 2 xl605 2 xl0 6 x48xl0" 12 ) i =205 /xH 

The oscillator must be able to tune over the frequency band 

(525+470) = 995 kHz to (1605+470) = 2075 kHz 

This is a frequency ratio of 2075/995 or 2.085 : 1 and requires 
a capacitance ratio of 2.085 2 or 4.349 : 1. This capacitance 
ratio must be obtained using the same tuning capacitor as 
before and so either the minimum capacitance must be in- 
creased or the maximum capacitance must be decreased. 

Use of a Trimmer Capacitor 

Let the minimum capacitance needed in the local oscillator be 
x pF then 

4.349x = x + 400 

x = 400/3.349=1 19.4 pF^l 19 pF 

The minimum capacitance of the oscillator tuning circuit can 
be increased to this value by connecting a trimmer capacitor in 
parallel with the variable capacitor. Assuming the minimum 
capacitance of the variable plus strays to be the same as in the 
r.f. circuit, i.e. 40 pF, then a trimmer capacitor of 119 — 40 = 
79 pF is needed (see Fig. 9.7). The tuning inductance L 2 is 


Fig. 9.7 Use of a trimmer capacitor 
in the oscillator 





|205/jH 79pFS 

k M 

! 40-440 L 2 

Denotes ganging 

easily calculated using L 2 = l/4-n- 2 /? (max) C mi „ and is equal to 
49.4 jiH. Unfortunately, correct tracking will not be main- 
tained between the r.f. and local oscillator circuits as the 
receiver is tuned over its frequency bands. 


A superheterodyne radio receiver employs ganged capacitors in its 
aerial and local oscillator circuits with an additional parallel capacitor 
in the local oscillator circuit. As the capacitance in the signal circuit 
varies from 80 pF to 320 pF the receiver is tuned from 1200 kHz to 
600 kHz. If the local oscillator capacitance variation is from 160 pF to 
400 pF, and the intermediate frequency is 433 kHz, what is (i) the 
frequency to which the receiver is tuned when the signal circuit 
capacitance is 200 pF, (ii) the local oscillator frequency when the local 
oscillator capacitance is 280 pF, (iii) the tracking error when the 
capacitance is at the mid-point of its range? (C & G) 


For both the r.f. and the local oscillator circuits the maximum 

frequency corresponds to the minimum capacitance. Therefore, 

(i) 1200x10 3 = 1/2ttV(Lx80x10" 12 ) (9.4) 

/=l/2W(Lx200xlO -12 ) (9.5) 

Dividing equation (9.4) by equation (9.5), 

1200xl0 3 _ /200 

/ ~ V 80 

/=1200xl0 3 /1.581 =758.95 kHz (Ans.) 

(ii) Maximum oscillator frequency = 1200+433 = 1633 kHz 

1633 x 1 3 = 1/2tts/(L x 160 x 10 -12 ) 

/ = 1 /2ttV(L x 280 x 10" 12 ) 

1633 xlO 3 /280 

\ =1.323 



f V160 

/= 1633 x 10 3 /1.323 = 1234.43 kHz 


Fig. 9.8 Use of a padder capacitor 

(iii) The midpoint of the capacitance range corresponds to the values 
used in parts (i) and (ii). Therefore, 

Tracking error = 1234.43 kHz-(758.95+433) kHz 
= 42.48 kHz (Am.) 

Use of a Padder Capacitor 

The alternative method of reducing the capacitance ratio in 
the local oscillator circuit is the connection of a padder 
capacitor in series with the tuning capacitor. Suppose that the 
same tuning capacitor and frequencies as before are used. The 
minimum and maximum capacitances are then 40 pF and 
440 pF. If the padder capacitor is denoted by C p then, since 
the required capacitance ratio is 4.349 : 1, 

^^ = 4.349x^2^ 
440 +C P 40+C p 

440 x 40 + 440C P = 4.349 x 40 x 440 + 4.349 x 40 C p 

C p (440 -4.349x40) = 40x440(4.349-1) 


p "440-4.349x40 

= 221.6 pF = 222 pF 

Fig. 9.8 shows the arrangement of the r.f. and local oscillator 


l /■■ 





40-440 pF 


Denotes ganging 

The total capacitance of the circuit will now vary from 

40x222 „„ nrt „ 440x222 , ,„ « ^ 

or 33.89 pF to or 147.55 pF 

40 + 222 


The inductance L 3 required to tune the circuit can be calcu- 
lated using the maximum frequency of 2075 kHz and the 
minimum capacitance of 33.89 pF (or vice versa). Thus, 

L 3 = 1/(4tt 2 x 2075 2 x 10 6 x 33.89 x 10~ 12 ) = 173.6 fiH 



Again, correct tracking is not obtained over most of the tuning 
range of the receiver. 

The tracking error does not have much effect on the quality 
of the audio output signal since the tuning of the receiver 
positions the wanted signal into the middle of the passband of 
the i.f . amplifier. This means that the intermediate frequency is 
correct and the tracking error exists in the r.f. stage. The error 
in tuning the r.f. stage has little, if any, effect upon the 
adjacent channel selectivity but both the sensitivity and the 
image channel rejection are worsened. Tracking is not a prob- 
lem in v.h.f. receivers because the required frequency and 
capacitance ratios are small. 

Fig. 9.9 Tracking curves 





>■ 1000 


Zero tracking error at A, B and C 

Ideal oscillator curve 

r.f. stage 

Increasing in this direction ►- 

Tuning capacitance 

If both a trimmer and a padder capacitor are used, three- 
point tracking can be obtained and the tracking error reduced 
to a small figure. Three-point tracking is illustrated by the 
curves of Fig. 9.9: the r.f. circuit and the ideal oscillator curves 
are always separated by a frequency difference equal to the 
intermediate frequency of the receiver. The practical curve, 
shown dotted, has zero tracking error at the three points 
marked A, B and C; elsewhere the error is small. 


The Intermediate Frequency Amplifier 

The purpose of the i.f. amplifier in a superheterodyne radio 
receiver is to provide most of the gain and the selectivity of the 
receiver. Most broadcast receivers utilize the impedance/fre- 
quency characteristics of single- or double-tuned circuits to 
obtain the required selectivity, but many receivers use ceramic 
filters, particularly when an integrated circuit is used as the i.f. 
amplifier. Narrow-band communication receivers must possess 
very good selectivity and very often employ one or more 
crystal filters to obtain the necessary gain/frequency response. 
The use of a ceramic or a crystal filter to provide the selectivity 
of a radio receiver offers a number of advantages over the use 
of L-C networks: 

(a) A very narrow bandwidth can be obtained. 

(b) The selectivity of the receiver does not depend upon the 
correct alignment of the i.f. amplifier. 

(c) The selectivity of the filter is not affected by the applica- 
tion of automatic gain control to the receiver. 

Choice of Intermediate Frequency 

The main factors to be considered when choosing the inter- 
mediate frequency for a superheterodyne radio receiver are 
(a) the required i.f. bandwidth, (b) interference signals, (c) the 
required i.f. gain and stability, and (d) the required adjacent 
channel selectivity. 

The minimum bandwidth demanded of an i.f. amplifier 
depends upon the type of receiver and is about 9 kHz for an 
amplitude-modulation broadcast receiver. Since the bandwidth 
of a coupled-tuned circuit is proportional to its resonant 
frequency {B=\llf IQ) the larger the bandwidth required the 
higher must be the intermediate frequency. The intermediate 
frequency should not lie within the tuning range of the re- 
ceiver, so that the r.f. stage can include an i.f. trap to prevent 
i.f. interference. However, to simplify the design and construc- 
tion of the i.f. amplifier, the intermediate frequency should be 
as low as possible. Adequate adjacent channel selectivity is 
easier to obtain using a low intermediate frequency, but on the 
other hand, image channel rejection is easier if a high inter- 
mediate frequency is selected. 

The intermediate frequency chosen for a receiver must be a 
compromise between these conflicting factors. Most 
amplitude-modulated broadcast receivers employ an inter- 
mediate frequency of between 450 and 470 kHz; but 
frequency-modulation broadcast receivers, which require an 
i.f. bandwidth of about 200 kHz, use an intermediate fre- 
quency of 10.7 MHz. 


The Detector Stage and Automatic Gain Control 

The function of the detector stage in a radio receiver is to recover 
the information modulated onto the carrier wave appearing at 
the output of the i.f. amplifier. Most a.m. broadcast receivers 
use the diode detector because of its simplicity and good 
performance but i.e. versions often use the transistor detector. 
The transistor detector is not often used in discrete form for 
broadcast receivers because of its limited dynamic range, but it 
is used in v.h.f. communication receivers where its ability to 
provide an amplified a.g.c. voltage and its gain are an advan- 
tage. Most f.m. broadcast receivers use the ratio detector but 
high-quality broadcast receivers may use the Foster-Seely 
circuit; when the latter circuit is used the detector must be 
preceded by a limiter stage. When the detector stage is part 
of an integrated circuit, the quadrature detector or, less often, 
the phase-locked loop detector is used. High-frequency 
i.s.b./s.s.b. communication receivers generally use some form 
of balanced or product demodulator. 

Automatic Gain Control 

The field strength of the wanted signal at the aerial is not 
constant but fluctuates widely because of changes in propaga- 
tion conditions. Automatic gain control (a.g.c.) is applied to a 
radio receiver to maintain the carrier level at the input to the 
detector at a more or less constant value even though the level 
at the aerial may vary considerably. A.G.C. ensures that the 
audio output of the receiver varies only as a function of the 
modulation of the carrier and not with the carrier level itself. 
The use of a.g.c. also ensures that a large receiver gain can be 
made available for the reception of weak signals without 
causing overloading of the r.f. amplifier stages, with conse- 
quent distortion, by strong signals. Further, a reasonably con- 
stant output level is obtained as the receiver is tuned from one 
station to another. 

In an f.m. receiver automatic gain control is often fitted to 
ensure (a) that the signal arriving at the input terminals of the 
limiter is large enough for the limiting action to take place and 
(b) that overloading of the r.f. and i.f. amplifier stages does not 
occur. In some cases the automatic gain control of an f.m. 
receiver may mean switching into the r.f. stage of one or more 
stages of an attenuator. 

The basic idea of an a.g.c. system is illustrated by Fig. 9.10; a 
direct voltage is developed, either in the detector stage or in 
the amplitude limiter, that is proportional to the amplitude of 
the carrier signal appearing at the output of the i.f. amplifier. 
The gain of a transistor amplifier is a function of the d.c. 


Auxiliary a.g.c 












Main a.g.c. 

Fig. 9.10 Application of automatic 
gain control to a superheterodyne 
radio receiver 

operating point of the transistor; hence if the a.g.c. voltage is 
applied to each of the controlled stages to vary their bias 
voltages, the gains of these stages will be under the control of 
the a.g.c. system. The polarity of the a.g.c. voltage should be 
chosen so that an increase in the carrier level, which will 
produce an increase in the a.g.c. voltage, will reduce the gain 
of each stage. This will, in turn, reduce the overall gain of the 
receiver and tend to restore the carrier level at the detector to 
its original value. Conversely, of course, if the carrier level 
should fall, the gain of the receiver will be increased to tend to 
keep the level at the detector very nearly constant. Another 
a.g.c. loop, known as auxiliary a.g.c, is often provided to give 
extra control of the gain of the receiver and to limit the 
amplitude of strong input signals to prevent overloading of the 
r.f. amplifier and the consequent distortion and cross- 
modulation. In many f.m. receivers only auxiliary a.g.c. is 

Main A.G.C. 

Automatic gain control systems are either of the simple or 
the delayed type. In a SIMPLE A.G.C. SYSTEM the a.g.c. 
voltage is developed immediately a carrier voltage appears at 
the output of the i.f . amplifier. This means that the gain of the 
receiver is reduced below its maximum value when the wanted 
signal is weak and the full receiver gain is really wanted. This 
disadvantage of the simple a.g.c. system can be overcome by 
arranging that the a.g.c. voltage will not be developed until the 
carrier level at the detector has reached some pre-determined 
value — generally that at which the full audio-frequency power 
output can be developed. Such a system is known as a DE- 
LAYED A.G.C. SYSTEM. Fig. 9.11 shows, graphically, the 
difference between simple and delayed a.g.c. systems; in addi- 
tion the performance of the ideal a.g.c. system is shown. It is 
evident that the ideal system is one in which no a.g.c. voltage 
is produced until the input voltage to the receiver exceeds 
some critical value and thereafter keeps the output level of the 
receiver perfectly constant. For economic reasons the majority 
of broadcast receivers use simple a.g.c. 


No a.g.c. 



a.f. output 




Delayed a.g.c. j 







. _ — ^Simple a.g.c. j 

\ ! 

Ideal a.g.c. j_ 

a.f.c. circuit 


Input wanted signal voltage 

Fig. 9.12 Application of automatic 
frequency control to a radio receiver 

Fig. 9.11 Automatic gain control 

Automatic Frequency Control 

The intermediate frequency bandwidth of a communication 
receiver operating in the u.h.f. band is only a small percentage 
of the carrier frequency. A relatively small percentage error in 
the frequency of the local oscillator may lead to the wanted 
signal being wholly or partly rejected by the selectivity of the 
i.f. amplifier. Some of the necessary frequency stability can, 
however, be obtained by a suitable choice of the type of 
oscillator to be used but the most stable types of oscillator 
cannot be tuned to different frequencies. The required fre- 
quency stability can be obtained by the use of AUTOMATIC 
FREQUENCY CONTROL (a.f.c). To avoid distortion of the 
output signal caused by mistuning, many f .m. broadcast receiv- 
ers also have a.f.c. fitted. 

The basic principle of an a.f.c. system is shown by Fig. 9.12. 
The output of the i.f. amplifier is passed through an amplitude 
limiter and is then applied to the input terminals of a dis- 
criminator. The input circuit of the discriminator is tuned to 
the nominal intermediate frequency of the receiver and so the 
circuit produces an output voltage of zero whenever the inter- 
mediate frequency is correct. If, however, the intermediate 
frequency differs from its nominal value a direct voltage will 
appear at the output of the discriminator. The polarity of this 
direct voltage will depend upon whether the intermediate 
frequency is higher than, or lower than, its nominal value. 
Thus if a negative voltage is produced by an increase in 
frequency, then a fall in the intermediate frequency will result 
in a positive direct voltage at the output of the discriminator. 
The direct voltage is taken to a voltage-variable capacitance, 
the magnitude of which is a function of that voltage. The 
variable capacitance is a part of the frequency-determining 


network of the local oscillator and so a change in its value will 
alter the frequency of oscillation. The voltage-dependent 
capacitance can be provided in a number of ways but the most 
common is the use of a varactor diode (Fig. 9.13). The 
varactor diode D is connected in parallel with the tuned circuit 
and so it provides a part of the total tuning capacitance of the 
local oscillator. 

Fig. 9.13 Varactor diode control of 
local oscillator frequency 

tuned circuit 


An a.f.c. system incorporates a discriminator with an output-, 
voltage/input-frequency characteristic of 1 V/3 kHz and a voltage- 
controlled oscillator whose output-frequency/input-voltage charac- 
teristic is 15 kHz/V. Calculate the tuning error with the a.f.c. system 
operative if without the a.f.c. the frequency error would have been 
24 kHz. 


Let the final frequency error be / kHz. Then the d.c. output voltage of 
the discriminator is //3 volts arid this voltage will cause the frequency 
of the oscillator to be shifted by (//3) x 15 = 5/ kHz. The final tuning- 
error is equal to the original error minus the frequency correction 
provided by the a.f.c. system. Therefore, 

f=24-5f or / = 4kHz (Ans.) 

The PULL-IN or CAPTURE RANGE of an a.f.c. system is 
the maximum frequency error that can be reduced by the 
system. It is obviously necessary that an a.f.c. system is 
designed so that the capture range is larger than the maximum 
expected drift in the oscillator frequency. The HOLD-IN 
RANGE is the band of frequencies over which the controlled 
oscillator frequency can suddenly change without the control 
exerted by the a.f.c. system being lost. 

Frequency Synthesis 

Modern communication receivers often obtain the required 
degree of frequency stability by deriving the local oscillator 
frequency from a frequency synthesizer instead of using a.f.c. 


The Audio-frequency Stage 

The function of the audio -frequency stage of a radio receiver is 
to develop sufficient a.f. power to operate the loudspeaker or 
other receiving apparatus. The a.f. stage will include a volume 
control and sometimes treble and bass controls. The a.f. stage 
may also include a squelch or muting facility. A sensitive 
receiver will produce a considerable output noise level when 
there is no input signal because there will then be no a.g.c. 
voltage developed to limit the gain of the receiver. The noise 
unavoidably present at the input terminals of the receiver then 
receives maximum amplification. This noise output can cause 
considerable annoyance to the operator of the receiver and, to 
reduce or eliminate this annoyance, a SQUELCH circuit is 
fitted which disconnects, or severely attenuates, the gain of the 
a.f. amplifier whenever there is no input signal present. 

The Double Superheterodyne Radio Receiver 

To obtain good adjacent channel selectivity, the intermediate 
frequency of a superheterodyne radio receiver should be as 
low as possible, but to maximize the image channel rejection 
the intermediate frequency must be as high as possible. For 
receivers operating in the low and medium frequency bands it 
is possible to choose a reasonable compromise frequency. In 
the h.f. band it may prove difficult to select a suitable fre- 
quency and for this reason many receivers use two, or more 
rarely, three or four different intermediate frequencies. 

The first intermediate frequency is chosen to give good 
image channel rejection ratio and the second frequency is 
chosen for good adjacent channel selectivity. Typically, the 
first intermediate frequency might be 3 MHz and the second 
intermediate frequency 100 kHz, although in modern receivers 
there is a tendency to use a very high first intermediate 
frequency, such as 35 MHz, to give a very good image rejec- 
tion (usually the second intermediate frequency is then about 

The disadvantages of the double superheterodyne principle 
are the extra cost and complexity involved and the generation 
of extra spurious frequencies because there are two stages of 
mixing. The most serious of these new frequencies is the 
second/image channel frequency. 


Fig. 9.14 Independent sideband 

106 kHz 

ch. A 




0-6 kHz 

-100 kHz 


1 1 


ch. B 







0-6 kHz 


*- s«- iud khz 
3.106 MHz plus others 

, i 

F 2 



100 kHz 













3 MHz 


100 kHz 



To a.g.c. and 
' ' a-f-c. circuitry 



Communication Receivers 

Fig. 9.14 gives the block schematic diagram of an i.s.b. com- 
munication receiver. The received signal, in the 4-27.5 MHz 
frequency band, is first amplified and then frequency changed 
to the standard frequency band of 3.094-3.106 MHz. After 
further amplification, the signal is translated to the 94- 
106 kHz band. Channel filters, F l and F 2 , select the signals 
appropriate to the channels, and the selected signals are then 
demodulated to obtain the original audio-frequency signal. A 
narrow passband filter tuned to 100 kHz selects the pilot 
carrier and applies it to the a.g.c. and a.f.c. circuitry of the 

A more modern type of i.s.b. receiver now in use by the 
British Post Office is shown in block diagrammatic form in Fig. 
9.15. It can be seen that this receiver uses four stages of 
mixing and i.f. amplification. The first intermediate frequency 
is above the tuning range of the receiver (3-27.5 MHz). Fre- 
quency synthesis is used to derive the first and the second/local 
oscillator frequencies, the synthesizer being controlled by a 
memory unit. The memory unit in conjunction with a digital 
circuit causes the appropriate band-pass filter to be switched 
into the aerial circuit to broadly select the wanted signal. Six 
filters are available covering, respectively, the frequency bands 
3-4 MHz, 4-6 MHz, 6-9 MHz, 9-13 MHz, 13-19 MHz and 
19-27.5 MHz. Selection of the wanted signal is achieved by the 
first, second and third i.f. amplifiers. 










'<o er 

*• 2 

<D ~ 

— c 



oi § 


3 kHz 






Class B 

a.f. push-pull 





Class C 



Class C 








10.7 MHz 

460 kHz 

3 kHz 











10.24 MHz 








a.g.c. voltage 

Fig. 9.16 A v.h.f. amplitude modulated transreceiver 

Many amplitude- and frequency-modulated communication 
receivers operating in the v.h.f. and the u.h.f . bands are mobile 
installations and are operated from the same aerial as the 
associated transmitter. The block schematic diagram of a v.h.f 
transreceiver is shown in Fig. 9.16. The transmitter is only 
connected to the aerial when the aerial switch is depressed. 
This switch is very often mounted on the telephone handset. 
Transmitters of this type have been described in Chapter 8; 
note that the transmitter can operate on any one of four 
channels by selection of the appropriate crystal oscillator. The 
receiver is of the double superheterodyne type, using first and 
second intermediate frequencies of 10.7 MHz and 460 kHz 
respectively. The first intermediate frequency is fairly stan- 
dard. A separate a.g.c. detector is used and this allows delayed 
a.g.c. to be applied to the controlled stages. Finally, squelch 
(or muting) is applied to the a.f. section of the receiver to 
prevent its operation when no signal is being received. 



3 kHz 




Frequency Tuned 
modulator amplifier 


Class C 





Class C 

















Fig. 9.17 A v.h.f. frequency modulated transreceiver 

The block schematic diagram of a frequency-modulated 
transreceiver, which uses a frequency synthesizer to derive the 
wanted mixer frequencies, is shown in Fig. 9.17. Two stages of 
mixing and of i.f. amplification are provided, the selectivity of 
the second amplifier being provided by a crystal filter. 

For both the transreceivers shown in Figs. 9.16 and 9.17 the 
choice of frequencies at various points in the circuit depends 
upon the frequency band in which the equipment is designed 
to operate. The various mobile bands are given elsewhere 

Measurement of Performance of Amplitude Modulation 

A number of measurements can be carried out to determine 
the performance of a superheterodyne radio receiver. Some of 
these tests are appropriate for both amplitude- and frequency- 
modulated receivers while others only apply to one type of 
receiver. In this book only the more important of the amp- 
litude modulation receiver measurements will be described; 
these are (a) sensitivity, (b) noise factor, (c) adjacent channel 
ratio, and (d) image channel response ratio. 







Fig. 9.18 Measurement of radio re- 
ceiver sensitivity 

(a) Sensitivity 

The sensitivity of an amplitude modulation radio receiver is 
the smallest input signal voltage, modulated to a depth of 30% 
by a 1000 Hz (or 400 Hz) tone, needed to produce 50 mW 
output power with a signal-to-noise ratio of 20 dB. 

The circuit used to carry out a sensitivity measurement is 
shown in Fig. 9.18. The signal generator is set to 30% modula- 
tion depth at the required frequency of measurement and its 
output voltage is set to a value about 10 dB above the ex- 
pected sensitivity. The audio-frequency gain of the receiver is 
then set to approximately its half -maximum position and the 
receiver is tuned to the measurement frequency. The signal 
generator frequency is then varied slightly to give the max- 
imum reading on the output power meter. The input voltage 
producing the necessary audio output condition can now be 
determined. The input voltage is varied until the power meter 
indicates 50 mW; then the signal generator modulation is 
switched off and the power meter indication is noted, say 
PmW. The output signal-to-noise ratio is now 10 log 10 x 
(50/P) dB. 

If this ratio is not equal to the required 20 dB the modula- 
tion of the signal generator is switched on again and the input 
voltage to the receiver is increased or decreased as approp- 
riate. The a.f. gain is adjusted to obtain 50 mW indication on 
the power meter before the modulation is again switched off 
and the new signal-to-noise ratio determined. This procedure 
is repeated until the required output power of 50 mW is 
obtained together with 20 dB signal-to-noise ratio. The input 
signal voltage giving the required output conditions is the 
sensitivity of the receiver. 

(b) Noise Factor 

The noise factor F of a radio receiver is the ratio 

Noise power appearing at the output of the receiver 
~ That part of the above which is due to thermal 
agitation at the input terminals 

This definition of noise factor is, for most conditions, equival- 
ent to the previously quoted, equation (9.3), meaning of noise 
factor, i.e. 






Fig. 9.19 Measurement of radio re- 
ceiver noise figure 

F = 

Input signal-to-noise ratio 
Output signal-to-noise ratio 


Fig. 9.19 shows the circuit used for the measurement of the 
noise factor of a receiver. With the noise generator switched 
off, the indication of the power output meter is noted. The 


noise generator is then switched on and, without altering any 
of the receiver controls, its noise output is increased until the 
indication of the power meter is exactly double its previous 

The noise output of the generator is directly proportional to 
the current indicated by an integral milliammeter and so the 
noise factor of the receiver is equal to 



where I a is the indication of the milliammeter and R is the 
(matched) impedance of the receiver and the noise generator. 
If, as is often the case at v.h.f. and at u.h.f., R = 50 il, the 
noise factor of the receiver is equal to the milliammeter 


In a measurement of the noise factor of a 50 fl input impedance radio 
receiver the reading of the output power meter is doubled when the 
noise generator's milliammeter indicates 6 mA. Calculate the noise 
factor of the receiver in dB. 


F = 6 or 10 log 10 6 = 7.78 dB (Ans.) 

Fig. 9.20 Measurement of radio re- 
ceiver adjacent channel response 

(c) Adjacent Channel Selectivity 

The selectivity of a radio receiver is its ability to select the 
wanted signal from all the unwanted signals present at the 
aerial. The selectivity curves given in Fig. 9.5 indicate how 
well the receiver rejects unwanted signals when the wanted 
signal is not present. This is, of course, not of prime interest 
since the important factor is the adjacent channel voltage 
needed to adversely affect reception of the wanted signal. This 
feature of a receiver is expressed by its adjacent channel 
response ratio which can be measured using the arrangement 
shown in Fig. 9.20. 













With signal generator 2 producing zero output voltage, 
signal generator 1 is set to the required test frequency and 
then is modulated to a depth of 30%. With the input signal 
voltage at 10 mV, the a.f. gain of the receiver is adjusted to 
give an audio output power greater than 50 mW but below the 


Fig. 9.21 Selectivity characteristic 
of a radio receiver 

10 mV 

Frequency off-tune 

overload point. The modulation of signal generator 1 is then 
switched off. Signal generator 2 is then set to a frequency that 
is 9 kHz above the test frequency and is modulated to a depth 
of 30%. The output voltage of signal generator 2 is then 
increased until the audio output power is 30 dB less than the 
previous value. The adjacent channel response ratio is the 
ratio of these voltages. The measurement can be carried out at 
a number of other frequencies and the results plotted (Fig. 

(d) Image Channel Response Ratio 

The image channel response ratio (or rejection ratio) is the 

/ Input voltage at image frequency X 
VInput voltage at signal frequency/ 

to produce the same audio output power. The measurement 
can be carried out using the circuit given in Fig. 9.18. The 
signal generator and the receiver are each tuned to the test 
frequency and the input voltage is adjusted to give an audio 
output power of 50 mW. Then, without altering any of the 
receiver controls, the frequency of the signal generator is 
altered to the image frequency. The input voltage is then 
increased until 50 mW audio output power is again registered 
by the power meter. The image response ratio is then given by 
the ratio of the two necessary input voltages, expressed in dB. 



9.1. What is meant by the terms ganging and tracking when applied 
to the alignment of a superheterodyne receiver? A receiver 
having an intermediate frequency of 465 kHz is required to 
tune over a range of 600 kHz to 1800 kHz with a ganged 
variable capacitor having a range of 320 pF per section. Calcu- 
late the values of (a) the minimum capacitance needed in the 
r.f. circuit, (b) the inductance required in the r.f. circuit, (c) the 
padding capacitance required in the local oscillator circuit as- 
suming that the minimum value of the capacitance is the same 
as that found in (a), and (d) the inductance required to tune the 
local oscillator. (C & G) 

9.2. With the aid of a block schematic diagram, describe the princi- 
ple of operation of a superheterodyne receiver suitable for 
amplitude-modulated sound broadcast reception. What are the 
reasons for the use of a tuned r.f. amplifying stage? Define the 
terms (a) sensitivity and (b) image channel response ratio in 
relation to the performance of a superheterodyne radio re- 
ceiver. Why is the image channel response generally lowest 
when the receiver is tuned to the highest frequency in its range? 

9.3. A single superheterodyne receiver with an i.f . of 465 kHz is 
tuned to an incoming sinusoidal signal of 1000 kHz. Assume 
the oscillator frequency to be above the signal frequency. What 
signal appears in the audio output if another unmodulated 
signal appears in the aerial at a frequency of (a) 1932 kHz, (b) 
1008 kHz, and (c) 469 kHz? For each of these frequencies state 
what factor in the receiver design affects the level of the output 
signal. Explain the advantages of a double superheterodyne 
receiver over a single superheterodyne receiver. (C & G) 

9.4. Explain the meaning of the terms and the need for (a) ganging, 
(fc) padding, (c) trimming in a superheterodyne receiver. The 
capacitor in the r.f. tuned circuit of a superheterodyne receiver 
varies from 60 pF to 540 pF as the receiver tunes from 
1500 kHz to 500 kHz. The receiver has an i.f. of 465 kHz and 
the local oscillator frequency is above the signal frequency. 
What value of trimming capacitance should be added to an 
identical ganged capacitor in the tuning section of the local 
oscillator to obtain correct tracking at both ends of the fre- 
quency range? (C & G) 

9.5. With the aid of a block schematic diagram describe the applica- 
tion of automatic frequency control to an f.m. radio receiver. 
Why is a.f.c. more necessary at v.h.f. than at lower frequencies? 
An a.f.c. discriminator produces 1 V of control bias for a 
frequency error of 50 kHz and. the controlled oscillator is 
shifted by 250 kHz. Calculate the tuning error if the oscillator 
would have drifted 20 kHz from the correct frequency without 
a.f.c. (C & G) 

9.6. A superheterodyne receiver has an intermediate frequency of 
10.7 MHz, and the local oscillator frequency is above the signal 
frequency. The receiver covers the band of f.m. carriers spaced 
at 0.5 MHz intervals between 75 MHz and 97 MHz. Each of 
these carriers has a modulation index of 5, when the maximum 
modulating frequency is 15 kHz. 


(a) (i) What is the number of f.m. channels in the band? (ii) 
What is the minimum i.f. bandwidth required? (b) When the 
receiver is tuned to the carrier at 75 MHz, what is the band 
covered by (i) the image channel, (ii) the adjacent channel? (c) 
(i) Which carriers are most susceptible to image channel inter- 
ference from within the band? (ii) What are the frequencies of 
the interfering carriers? (C & G) 

9.7. (i) In what part of a superheterodyne receiver is image rejection 
provided? (ii) Why is image rejection needed? (iii) Is image 
rejection better at the high frequency end of the tuning range of 
the receiver or at the low-frequency end? (iv) Why is an r.f. 
amplifier not always used? (v) Why is the double- 
superheterodyne principle often employed? (vi) Quote common 
intermediate frequencies for such a receiver. 

9.8. Draw the block schematic diagram of a superheterodyne re- 
ceiver. Discuss the functions of each block. What are the 
advantages of using integrated circuits in a receiver? State some 
of the functional circuits which are currently available in i.e. 
form and draw a block diagram for a receiver using some, or 
all, of these i.c.s. 

9.9. A superheterodyne receiver has f lf = 470 kHz. It is tuned over 
the frequency band 500-1500 kHz. What range of frequencies 
must its local oscillator cover? What are (i) the lowest and (ii) 
the highest image frequencies? How can the image frequencies 
be suppressed? Draw a typical circuit, including waveband 

9.10. A superheterodyne radio receiver is tuned to 1.2 MHz and its 
local oscillator then operates at 1665 kHz. What is its inter- 
mediate frequency? Discuss the reasons leading to the choice of 
such a frequency for this purpose. 

9.11. Draw the block diagram of a superheterodyne receiver. Explain 
its operation. A receiver tunes to the band 90-100 MHz and 
has an i.f. of 10.7 MHz. Calculate (i) the range of frequencies 
over which the local oscillator is tuned and (ii) the maximum 
and minimum image frequencies. Which of these two frequen- 
cies are suppressed most efficiently? 

9.12. Explain the meanings of the following terms used with radio 
receivers: (a) selectivity, (b) sensitivity, (c) image channel re- 
sponse ratio. For each, state which part of the receiver deter- 
mines the characteristic. 

Draw the block diagram of a double superheterodyne re- 
ceiver; list the function of each block. Quote typical figures for 
the first and second intermediate frequencies, and hence deter- 
mine the frequencies of the two local oscillators when a 6 MHz 
signal is received. 

9.13. (a) What is meant by the terms (i) ganging, (ii) tracking when 
applied to the alignment of a superheterodyne receiver? 

(b) A receiver having an intermediate frequency of 465 kHz 
is required to tune over a range 550 kHz to 1650 kHz with a 
ganged capacitor which can be varied by 320 pF. Calculate the 
values of 

(i) the minimum capacitance required in the r.f. circuit 
(ii) the self-inductance required in the r.f. circuit 
(iii) the padding capacitance required in the local oscillator 
section, assuming that the minimum value of the variable 
capacitor is that determined in (i) 

(iv) the self-inductance required to tune the local oscillator 
circuit. (C & G) 


Short Exercises 

9.14. In a v.h.f. receiver the local oscillator frequency is 140 MHz 
and the first intermediate frequency is 10.7 MHz. Calculate (i) 
the signal frequency (ii) the image channel frequency. Assume 
the signal frequency is higher than the oscillator frequency. 

9.15. Briefly explain the advantages of double superheterodyne 
operation of a receiver over single-superheterodyne operation. 

9.16. State the factors affecting the sensitivity of a radio receiver. 

9.17. List the reasons why the local oscillator in a superheterodyne 
communications radio receiver should be of high frequency 

9.18. Why is it usual to provide automatic gain control for an a.m. 
radio receiver? Why is a.g.c. not always applied to a f.m. 

9.19. What is the function of the limiter in an f.m. receiver? In what 
stage of the receiver might limiting be provided? 

9.20. What is meant by squelch or muting as applied to radio receiver 
and why is it often applied to communication receivers? Why is 
it not applied to a.m. broadcast receivers? 

9.21. What is meant by the terms ganging and three-point tracking 
when applied to a superheterodyne radio receiver? 

9.22. List the factors which influence the choice of intermediate 
frequency for a radio receiver. 

9.23. Why is it desirable for radio receivers operated at frequencies 
above about 3 MHz to be provided with r.f . gain? 

9.24. An f.m. receiver which is tuned to a frequency of 93 MHz is 
found to receive interference from a strong signal which has a 
frequency of 87.65 MHz. What is the name for this type of 
interference? (part C & G) 


Radio Receiver Circuits 


The principles of operation of the superheterodyne radio 
receiver have been discussed in the previous chapter by con- 
sidering the various sections of the receiver as blocks perform- 
ing particular functions. The circuits of the various kinds of 
detector have been discussed in Chapter 2 while radio- and 
audio-frequency amplifiers and oscillators are covered in a 
companion volume [EIII]. In this chapter the circuitry and 
principles of operation of some further radio receiver circuits 
will be given, namely mixers, crystal and ceramic filters, au- 
tomatic gain control, and squelch or muting arrangements. 


A MIXER is a circuit whose function is to translate a signal 
from one frequency band to another. If a mixer incorporates an 
oscillator it is often known as a frequency changer. There are 
two basic methods by which mixers operate: either the signal 
and the output of a local oscillator are added together and 
then applied in series with a square-law device, or the two 
signals are multiplied together in a multi-electrode valve or a 
dual-gate m.o.s.f.e.t. 

An additive mixer must include a device having a non-linear 
input-voltage/output-current characteristic; this device may be 
a diode or a suitably biased f .e.t. or transistor. 

The output current of the non-linear device contains compo- 
nents at the following frequencies: 

(a) The signal frequency / s . 

(b) The sum and difference f ±f s of the signal and the local 
oscillator frequencies. 

(c) The local oscillator frequency f„. 



Signal L , c. 
voltage * v z 

Fig. 10.1 Transistor mixer 

Fig. 10.2 Self-oscillating mixer 

(d) The sum and difference of the local oscillator frequency 
and the frequencies of all the other components present 
at the input terminals of the receiver. 

(e) Various intermodulation and harmonic frequencies. 

The output circuit of the mixer is usually tuned to select the 
difference frequency f -f, and to reject all other components. 

The non-linear device may consist of a semiconductor diode 
or of a suitably biased f.e.t. or transistor. One possible 
TRANSISTOR MIXER circuit is shown in Fig. 10.1. The 
transistor is biased with a low collector current so that it is 
operated on the non-linear part of its characteristics. The local 
oscillator signal is introduced into the base-emitter circuit via 
the inductances L 5 and L 6 and the signal voltage is inserted in 
series with the oscillator voltage via inductors L x and L 2 . The 
collector current then contains the wanted difference fre- 
quency component plus various other components. The collec- 
tor circuit is tuned so that the wanted component is selected 
and all other frequencies are rejected. 

Many transistor radio receivers employ a SELF- 
OSCILLATING MIXER, or frequency changer, of the type 
shown in Fig. 10.2, because the circuit is cheaper for a 
comparable performance. Inductors L 3 , L 4 and L 6 , capacitors 
Q and C 2 , and the transistor form the oscillator part of the 
circuit. Energy is fed from the collector circuit to the L 6 -C 2 
circuit, which is tuned to resonate at the desired frequency of 
oscillation. The oscillatory current set up in inductor L 6 in- 
duces a voltage, at the oscillation frequency, into the emitter 


circuit of the transistor in series with the signal voltage. Mixing 
takes place because of the non-linearity of the transistor 
characteristics, and the difference-frequency component of the 
collector current is amplified by the transistor and then 
selected by the collector tuned circuit C^-L 3 . 

A transistor mixer is equivalent to a diode square-law mixer 
followed by a transistor amplifier. Mixing is possible at all 
frequencies where the emitter-base p-n junction of the trans- 
istor exhibits diode characteristics; it is not necessary for the 
transistor to have gain at the signal frequency. It is therefore 
possible to use a transistor for mixing at frequencies where it 
would be useless as an amplifier; the transistor must, of course, 
be able to amplify the difference frequency. 

Fig. 10.3 A v.h.f. mixer 


The two previous mixer circuits have both introduced the 
local-oscillator voltage into the emitter circuit. Other methods 
are possible, and Fig. 10.3 shows the circuit of a V.H.F. 
MIXER in which both signal and local-oscillator voltages are 
fed into the base circuit. L t and C 3 tune the input circuit of the 
mixer to the signal frequency, and Cj and C 2 match the 
local-oscillator and signal-frequency circuits to the mixer. L 2 is 
provided to prevent alternating currents from passing into the 
collector supply, and C 4 , L 3 match the mixer to the output 
circuit and select the difference-frequency component of the 
collector current. 

Important features of a mixer are (a) its conversion conduc- 
tance, given by 

/ difference frequency component of the output current N 
\ r.f. input signal voltage / 

and (ft) its cross-modulation performance. Cross-modulation is 
the transfer of the modulation of an unwanted carrier onto the 
wanted carrier, and it can occur in a mixer if its mutual 
characteristic includes a cubic term. The mutual characteristic 
of a field-effect transistor more nearly approaches the ideal 


Fig. 10.4 Square-law f.e.t. mixer 


II o 



C 6 ± fl : 

C 7 ± 


Fig. 10.5 


Dual-gate m.o.s.f.e.t. 

square law and consequently f.e.t.s are increasingly employed 
as mixers in modern circuitry. A typical f.e.t. mixer circuit is 
shown in Fig. 10.4 together with an example of an oscillator 
circuit which is often used at v.h.f. 



MUTIPLICATTVE MIXING can be achieved by applying 
the signal and the local oscillator voltages to the two inputs of 
a dual-gate m.o.s.f.e.t. and Fig. 10.5 shows a dual-gate 
m.o.s.f.e.t. mixer circuit. The oscillator voltage is applied to 
gate 1 of the m.o.s.f.e.t. and the signal voltage is applied to 
gate 2. The oscillator voltage varies the mutual conductance of 
the m.o.s.f.e.t. and, since I d = g m V s , the alternating drain cur- 
rent is proportional to the product of the instantaneous values 
of the signal and the local oscillator voltages. The drain 
current contains components at a number of different frequen- 
cies amongst which is the wanted difference f„ —f s component, 
Mutiplicative mixing possesses two advantages over additive 
mixing; firstly, the signal and local oscillator circuits are iso- 
lated from one another which prevents oscillator pulling taking 
place and, secondly, its conversion conductance is higher. On 
the other hand multiplicative mixing is a noisier process. 



signal Z.,5 CL 2 • S r 

A number of integrated circuits are available which include 
the mixing process amongst their functions. An integrated 
circuit can be obtained from several different manufacturers 
which will act as either a balanced modulator/demodulator or 
as a mixer. Fig. 3.11 shows a possible circuit arrangement if 
the modulating signal and carrier inputs are read, respectively, 
as the r.f. and local oscillator voltages. The output voltage of 
the circuit is then, of course, the required difference frequency 

Very often the mixer is included in the same package as 
several other circuits. For example, one i.e. contains an r.f. 
amplifier, a mixer, a local oscillator, an i.f. amplifier and an 
a.g.c. detector. With any linear integrated circuits any neces- 
sary inductors and capacitors and large-value resistors must be 
provided externally. Fig. 10.6 shows a simplified example of 
this. The gain/frequency characteristics of the r.f. and i.f. 
amplifiers and the mixer are determined by the tuned circuits 
shown. The a.g.c. voltage line must have a particular time 
constant and this is provided by capacitor C 7 . 



2 ^ 
<f Q3 


J L Mixer 

49 9 








99 98 

\t-n c 7 :: 

Earth supply • 


"X - 

Fig. 10.6 Use of an integrated circuit in a radio receiver 






c 2 

Fig. 10.7 Electrical equivalent cir- 
cuit of a piezo-electric crystal 

Crystal and Ceramic Filters 

The principles of operation of piezo-electric cystals have been 
discussed in another volume [TSII] and in this section of the 
book some practical radio applications will be considered. 

The electrical equivalent circuit of a piezo-electric crystal is 
shown in Fig. 10.7; the inductance L represents the inertia of 
the crystal, capacitance Cj represents the crystal's compliance 
(1/stiffness) and the resistance R provides losses which are 
equivalent to the frictional losses of the crystal. Lastly, the 
shunt capacitor C 2 is the actual electrical capacitance of the 
crystal. A series-parallel circuit of this kind has two resonant 
frequencies, one is the resonant frequency of the series circuit 
L-C x -R and the other is the frequency at which parallel 
resonance occurs between shunt capacitor C 2 and the net 
(inductive) reactance of the series arm. Obviously, the parallel- 
resonant frequency is higher than the frequency of series 
resonance. The crystal will pass, with little attenuation, all 
frequencies in between the series and parallel resonant fre- 
quencies. Often this bandwidth is too narrow and when this is 
the case it can be widened by connecting an inductor of 
suitable value in series with the crystal. The added inductance 
has this effect because it will reduce the series-resonant fre- 
quency of the crystal without affecting its parallel-resonant 
frequency. Usually, this technique is only employed at the 
lower frequencies since when the centre frequency is high the 
bandwidth, as a percentage of the centre frequency, is likely to 
be wide enough. 

-O Output 

Fig. 10.8 Crystal filter 

A CRYSTAL FILTER circuit is shown in Fig. 10.8. The 
crystal is chosen to be one whose series-resonant frequency is 
equal to the required passband's lowest frequency. The 
parallel-resonant frequency of the crystal, and hence the upper 
passband frequency, is adjusted to the required figure by 
means of the variable capacitor C 3 . The selectivity of the 
circuit is partly determined by the load impedance of the filter 
and this can, to some extent, be varied by adjustment of C 4 
and/or R 1 . 


Fig. 10.9 A two-crystal filter 


4 rib dc xt, 2 c 4' 3 



Fig. 10.10 Crystal lattice filter 

A wider bandwidth filter can be obtained by the use of two 
crystals connected as shown in Fig. 10.9. The series-resonant 
frequencies of the crystals are chosen to differ from one 
another by a frequency equal to the wanted passband; this 
may be only a few hundred hertz if telegraphy signals are to be 
received or about 3 kHz for the reception of an s.s.b. signal. 
Capacitor C 4 is provided to allow for fine adjustment of the 
bandwidth provided. Even better selectivity characteristics can 
be obtained, but at greater expense, if four crystals are con- 
nected to form a lattice network (see Fig. 10.10). 

L Z\ i L 4 Output 

The two series crystals are chosen so that their common 
series-resonant frequencies lie within the required passband 
and they offer little attenuation to a narrow band of frequen- 
cies on either side of this frequency. The two parallel crystals 
are selected so that their parallel-resonant frequencies are 
equal to the series-resonant frequencies of the series crystals. 
They will not therefore shunt signals in the wanted passband. 
At frequencies outside the required passband the series cryst- 
als will have a high impedance and the parallel crystals will 
have a low impedance, and the network will offer considerable 

Complete crystal filter modules, suitable for use in the i.f. 
amplifier stage of a radio receiver, can be purchased from 
various manufacturers. 


Ceramic disc 


T 1 


$&M!&®}M l hree ' termi " a, 

J ceramic disc 



Fig. 10.11 Ceramic filter 

Fig. 10.12 Wideband amplifier 
using ceramic filters 

The piezo-electric effect is also obtained when a ceramic 
disc has electrode plates mounted on each of its two faces, the 
resonant frequencies and selectivity characteristic being deter- 
mined mainly by the shapes and dimensions of the electrodes 
and the disc. The make-up of a CERAMIC FILTER is shown 
in Fig. 10.11a; this type of filter, available as a complete 
sealed unit, is usually manufactured for use at one of the 
standard a.m. broadcast receiver intermediate frequencies. 
The input and output tuned circuits are both arranged to be 
resonant at the centre frequency of the desired passband. 
Ceramic filters for use at the higher frequencies, such as the 
standard 10.7 MHz intermediate frequency of many v.h.f. 
receivers, are usually of the three-electrode type shown in Fig. 
10.11 b. 

Both crystal and ceramic filters possess the following advan- 
tages over conventional tuned circuits: compact size, high 
stability and insensitivity to external magnetic fields. The 
ceramic filter is cheaper than the crystal filter and requires no 
tuning or alignment but, on the other hand, its passband loss is 
greater, it has a worse temperature stability, and its selectivity 
is not as great. Usually, ceramic filters are found in domestic 
broadcast radio receivers, particularly in conjunction with in- 
tegrated circuits, and crystal filters are used in communication 
receivers, for example as a channel filter in an i.s.b. receiver. A 
simplified example of the use of a ceramic filter is given in Fig. 
10.12; I.C.i is an r.f. wideband amplifier whose selectivity 
characteristic is shaped to the required i.f. amplifier response 
by the input and output ceramic filters F x and F 2 . All the 
necessary decoupling capacitors are supplied by external com- 
ponents because of the relatively high (0.01 /u.F) values re- 








o i.e., o 
-o o- 



c 2 ; 


c 3 



Automatic Gain Control 

The signals arriving at the input terminals of a radio receiver 
are subject to continual fading, and unless automatic gain 
control (a.g.c.) is used, the volume control will require con- 
tinual adjustment to keep the output of the receiver more or 
less constant. The function of an a.g.c. system is to vary the 
gain of a receiver to maintain a reasonably constant output 
power even though there are large variations in the input signal 
level. Thus the gain of the receiver must be reduced by the 
a.g.c. system when a large-amplitude input signal is received, 
and increased for a small input signal. The variation in the 
receiver gain also serves to prevent the output level changing 
overmuch as the receiver is tuned from one station to another, 
and it also avoids a.f. amplifier distortion caused by over- 
loading on larger input signals. 

Fig. 10.13 Derivation of simple 
a.g.c. voltage 

Simple A.G.C. 

The voltage appearing across the load resistor of a diode 
detector contains a direct component, the magnitude of which 
is directly proportional to the amplitude of the carrier voltage. 
This direct voltage is available for use as the a.g.c. voltage and 
can be fed to the controlled stages in the manner shown in Fig. 

f T, R 

^ — 1 — r— 








-| | o audio 

C 5 amplifier 


10.13. With the diode Dj connected as shown, the d.c. voltage 
developed across the load resistor R 2 is positive with respect 
to earth; if a negative voltage is required the diode Dj should 
be reversed. The a.g.c. voltage is fed to the controlled stages 
via a filter network C 3 — R t to remove the various alternating 
components that are superimposed upon it. The time constant 
of the filter should be chosen to ensure that the a.g.c. voltage 
will not vary with the modulation evelope but will respond to 
the most rapid fades to be expected. Typically, time constants 
of 0.05 to 0.5 seconds are used. 


Delayed A.G.C. 

A delayed a.g.c. system will not produce any a.g.c. voltage 
until the carrier level at the output of the detector is greater 
than some predetermined value. This means that the diode 
that produces the a.g.c. voltage must be biased into its non- 
conducting state by a bias, or delay, voltage of suitable mag- 
nitude. It is obvious that the signal diode cannot be biased into 
non-conduction and so it is necessary to use a separate diode 
for the a.g.c. voltage. 

D 2 



: Ly\ 

U 2 : 

:c 2 




c 3 : 

fl 4 




L c 4 


To a.f. 


:c 6 

Fig. 10.14 Derivation of delayed 


C5 T 
-« 1 — 

To controlled 

R 2 


a.g.c. voltage 


A large number of different circuits have been produced for 
delayed a.g.c. systems and Fig. 10.14 shows a typical circuit. 
The signal diode Dj is operated as a normal signal diode with 
a load resistor R t . The a.g.c. diode D 2 has a positive bias 
voltage VRJ(R 3 + R 4 ) at its cathode and will not conduct until 
the signal voltage appearing at its anode is greater than the 
bias voltage. When diode D 2 conducts, the a.g.c. voltage is 
developed across R 4 and is fed to the controlled stages via the 
filter network C s -R 2 - The a.g.c. diode is supplied from the 
collector of T, to obtain as large a voltage as possible. 

F.M. Receiver Main A.G.C. 

A main a.g.c. loop may sometimes be applied to an f.m. 
receiver to ensure that the signal level to the input of the 
limiter stage is always large enough for the limiting action to 
take place. The a.g.c. voltage can be obtained from the d.c. 
load capacitor of a ratio detector or, if a ratio detector is not 
used, from the limiter stage itself. Alternatively, a separate 
a.g.c. diode can be employed. 


Fig. 10.15 Gain/emitter current 
characteristic of a bipolar transistor 

Fig. 10.16 Reverse a.g.c. 

Applying the A.G.C. Voltage to the Controlled Stage 

The current gain of a bipolar transistor is a function of its 
emitter current and Fig. 10.15 shows a typical gain/emitter- 
current characteristic. At low values of emitter current the 
current gain of a transistor increases with increase in its 
emitter current in a more or less linear manner. The converse 
is true at high values of emitter current; an increase in the 
emitter current produces a fall in the current gain. Two 

7 8 9 

Emitter current (mA) 

methods are therefore available for varying the gain of an 
a.g.c. controlled stage in a radio receiver: increasing the gain 
by increasing the emitter current is known as reverse a.g.c, 
while increasing the gain by decreasing the emitter current is 
known as forward a.g.c. In either case the emitter current is 
most easily controlled by variation of the base-emitter forward 
bias voltage of the transistor since minimum power is then 
taken from the a.g.c. line. 



" 3 L T C3 

C 4± 


a.g.c. voltage 



Fig. 10.16 shows the application of REVERSE A.G.C. to a 
transistor tuned amplifier. The negative polarity a.g.c. voltage 
determines the forward bias voltage applied to the transistor 
Tj. An increase in the carrier level at the input to the detector 
stage will make the a.g.c. voltage become more negative. The 


Fig. 10.17 Forward a.g.c. 

base potential of T 1; relative to earth, will become less positive 
and the transistor will conduct a smaller emitter current. The 
voltage gain Of the amplifier will therefore fall and the carrier 
level at the detector will be reduced, tending to compensate 
for the original increase. 

Positive a.g.c. voltage 

When FORWARD A.G.C. is to be applied to an amplifier, 
a resistor is connected in series with the collector tuned circuit 
to increase the gain variation produced by a given a.g.c. 
voltage. A typical forward a.g.c. circuit is given in Fig. 10.17. 
When the positive a.g.c. voltage increases, because of an 
increase in the received carrier voltage, the forward bias of the 
transistor is also increased. The transistor conducts a larger 
current and so its current gain falls; the fall in gain is accen- 
tuated by the collector-emitter voltage also falling because of 
the increased voltage drop across the series resistor R 2 . 

The relative merits of reverse and forward a.g.c. are as 
follows. Reverse a.g.c. controls the gain of a stage by varying 
its emitter current; to reduce the gain the emitter current must 
be reduced and as a result the output resistance of the transis- 
tor increases. This, in turn, reduces the damping effect of the 
transistor on the collector tuned circuit and so reduces the 
bandwidth of the stage. The reduction in emitter current, and 
hence in the collector current, also has the effect of reducing 
the signal-handling capability of the stage — at the very time it 
is being called upon to handle a signal of larger amplitude. 
Conversely, with forward a.g.c. a decrease in the voltage gain 
of a stage is obtained by increasing the emitter and collector 
currents and is therefore associated with an increase in both 
the bandwidth and the signal handling capacity of the stagd. 
Also, the d.c. collector current taken from the supply is greater 


Fig. 10.18 Auxiliary a.g.c. 

d Main negative 
a.g.c. voltage 

with forward a.g.c. than with reverse a.g.c. and this may prove 
to be an embarrassment with battery-operated equipment. Fig. 
10.18 shows one way in which auxiliary a.g.c. can be applied 
to a receiver. The circuit operation is left as an exercise for the 

In an s.s.b./i.s.b. communication receiver, the a.g.c. system is 
often operated from a low-level pilot carrier which is filtered 
off from the wanted signal. If there is no pilot carrier, it is 
possible to derive an a.g.c. voltage from the received signal 
itself, either at the i.f. amplifier or the a.f. amplifier stages. 

Automatic Frequency Control 

The direct voltage needed to activate the automatic fre- 
quency control (a.f x.) system of a frequency-modulation radio 
receiver can be derived from the audio load capacitor of the 
ratio detector. Fig. 10.19 shows the essentials of a possible 
circuit arrangement. When the mean value of the intermediate 
frequency of the receiver is correct, the voltage appearing 
across the audio load capacitor C 4 has zero d.c. component 
and the varactor diode has the capacitance determined by the 
applied bias voltage. If the average value of the intermediate 
frequency should drift from its nominal value, the voltage 
developed across the audio load capacitor will have a direct 
component. This direct voltage is applied to the varactor diode 
to augment or oppose, depending on its polarity, the bias 
voltage and so vary the diode capacitance. This variation in the 


Fig. 10.19 Application of a.f.c. vol- 
tage in a radio receiver 

diode capacitance alters the frequency of the local oscillator in 
the direction necessary to reduce the error in the intermediate 
frequency. Capacitor C 3 and resistor JR 2 act as a low-pass filter 
to remove all alternating voltages from the a.f.c. line. 

Toa.f. amplifier 

Local oscillator 
tuned circuit 

Squelch or Muting 

A sensitive radio receiver will have a very high gain between 
its aerial terminals and its detector stage. When it is not 
receiving a carrier, and so develops zero a.g.c. voltage, its full 
voltage gain will be made available to amplify the noise 
unavoidably present at its input stage. As a result there will be 
a high noise level at the output of the audio amplifier which 
may cause considerable annoyance to the person operating the 
receiver. To reduce or eliminate this annoyance, the audio- 
frequency amplifier can be cut off, or its voltage gain severely 
reduced, whenever there is no input carrier signal; this is the 
function of a squelch, or a muting, circuit. 

Fig. 10.20 Squelch circuit 

A variety of different circuits are capable of providing the 
squelch action and an example of a squelch circuit is given in 
Fig. 10.20. When a carrier voltage is present at the detector 
input, a direct voltage, proportional to the carrier level, is 
applied to the base of transistor T t . The polarity of this direct 
voltage is such that T t is turned off and the collector potential 
of the transistor rises to +JB CC volts. The diode D t conducts 
and the audio-frequency output voltage of the signal detector 


is able to pass to the a.f . amplifier. With zero carrier voltage at 
the detector input, transistor T x is able to conduct and its 
collector potential falls to a lower positive value than is 
present at the junction of resistors R s and R 6 . Diode Dj is 
now biased into its non-conducting state and prevents noise 
voltages appearing at the detector output and passing onto the 
a.f. amplifier. 

Very often it is thought desirable for operational reasons for 
the squelch system to not cut off the a.f. amplifier but, instead, 
to reduce its gain to a low value. The output noise level can 
generally be varied by means of an adjustable squelch circuit 

10.1. (a) From what stage in a superheterodyne receiver is a.g.c. 
derived? (b) To what stages in a superheterodyne receiver can 
a.g.c. be applied? (c) Why is delayed a.g.c. preferred to simple 
a.g.c? (d) List the components in the circuit shown in Fig. 
10.21 which contribute to the a.g.c. action and indicate the 
function of each. How does this circuit compensate for a change 
in input signal level? (C & G) 

Fig. 10.21 

10.2. (a) Sketch the circuit of a transistor frequency changer stage 
with a following i.f . amplifier stage suitable for a medium-wave 
superheterodyne receiver. Describe the operation of these 
stages and show which elements in the circuit determine each of 
the three frequencies involved, (b) What is a typical gain for a 
single stage of the i.f. amplifier in a medium-wave amplitude- 
modulation broadcast receiver? (C & G) 

10.3. (a) Give reasons for the use of a.g.c. in a superheterodyne 
receiver designed for the reception of (i) a.m. signals (ii) f.m. 
signal, (b) Draw and explain a circuit that shows how the a.g.c. 
voltage can be applied to a transistor i.f. amplifier. 


10.4. With the aid of a circuit diagram explain the operation of the 
mixer and local oscillator of a transistor superheterodyne a.m. 
sound receiver. If the input to a mixer consists of two sinusoidal 
waves, at what frequencies do the significant components of the 
output occur? If a wanted sinusoidal wave and a sinusoidal 
wave at the image frequency are mixed with the local oscillator 
frequency of a receiver, explain why a large number of the 
output components of the mixer do not appear at the audio 
output. What does appear at the audio output? What appears at 
the output if the unwanted sinusoid is shifted by 2 kHz.? 


Fig. 10.22 


10.5. With reference to Fig. 10.22: (a) Why are D, and its as- 
sociated components included in the circuit? (b) Explain fully 
the operation of the section of the circuit which includes D^ 


10.6. With the aid of a graph explain the meaning and purpose of 
delayed a.g.c. Draw the circuit diagram of the i.f. amplifier and 
detector stages of a transistor superheterodyne receiver to show 
how simple a.g.c. is derived and applied. Why must the time 
constant in the a.g.c. feedback path be about 0.1 seconds? 


10.7. (a) Draw the circuit diagram of a ratio detector which will 
produce a suitable output to control the frequency of the 
receiver oscillator section, (b) Explain how the a.f.c. voltage is 
produced by the circuit given in (a) and describe how this 
voltage maintains the local oscillator at the required frequency. 

10.8. With the aid of a simplified circuit diagram explain how a.f.c. 
may be included in the design of a transistorized f .m. receiver. 
Include in the diagram a switch which will enable the a.f.c. to 
be switched out of circuit for tuning purposes and explain why 
this is desirable. (C & G) 


Fig. 10.23 


I — Mixer — 




7 8 
9 9 



| Power 













10.9. Fig. 10.23 shows the block schematic diagram of an integrated 
circuit that has been designed for use in a radio receiver. Draw 
a diagram showing the external components which are neces- 

Short Exercises 

10.10. Redraw Fig. 10.6 using ceramic filters. 

10.11. What is meant by the term squelch as applied to a radio 
receiver and describe how it works. 

10.12. Draw the circuit of a crystal i.f. filter and describe how it 

10.13. What is meant by automatic frequency control? Why can the 
frequency error never be completely eliminated by a.f.c? 

10.14. Draw the circuit diagram of a dual-gate m.o.s.f.e.t. mixer and 
explain its operation. 

10.15. Draw a circuit diagram showing how reverse a.g.c. may be 
applied to a p-n-p transistor stage. 

10.16. Draw a circuit diagram of a mixer that uses an integrated 
circuit. List the advantages of using integrated circuits. 


Wideband Line and 
Radio Systems 


The public transmission network of a country is used for the 
communication of many kinds of information such as com- 
merical quality speech, telegraphy, data signals and 
sound/ television signals for the broadcasting authorities. The 
network will contain audio-frequency circuits, pulse-code 
modulation systems and multi-channel systems routed over 
both coaxial cable and microwave radio -relay systems. The 
choice of transmission system for a particular route is deter- 
mined by a careful consideration of all the relevant factors 
such as the required transmission performance, the economics 
involved, and the nature of the terrain to be covered. Local 
lines and junctions whose length is less than about 16 km 
mainly operate as audio-frequency circuits, sometimes with 
two-wire amplification, although increasingly junctions use 
pulse code modulation. Longer-distance trunks are nearly all 
routed over one or more multi-channel telephony systems. 

International links between nearby countries are also estab- 
lished using both land coaxial and radio relay systems. Links 
between the United Kingdom and the Continent are mainly 
routed over submarine coaxial cables and, in the case of 
England-France, over radio relay systems also. Longer- 
distance intercontinental telephone circuits are routed over 
communication satellite systems and submarine coaxial sys- 
tems, augmented when and where necessary by high-frequency 
radio links using the sky wave mode of propagation. 

One other form of fixed radiocommunication system is used 
on routes where the terrain is too hostile, geographically or 
politically, for a coaxial cable (land or submarine) or a radio 
relay system to be used and the use of a communication 
satellite cannot be economically justified. Such tropospheric 
scatter systems can provide about a hundred speech circuits 


over a distance of up to about 600 km. The one example of the 
use of such a system in the United Kingdom is the links 
between oil rigs in the North Sea and the mainland of Scot- 

Land Coaxial Systems 

Coaxial multi-channel telephony systems play an important 
part in both national and international telecommunication 
networks. A number of different types of coaxial system are in 
current use in the United Kingdom and these are listed in 
Table 11.1. 

Table 11.1 

Number of channels Bandwidth in MHz 


2 700 

10 800 


12 channels 

5 groups 

15 supergroups 

1 2 supermastergroups 

Basic 60 channel 
312-552 kHz 

Basic 15 supergroup 

312-4028 kHz 
[900 channel system] 

Basic hypergroup 
10800 channels 
4432-59684 kHz 


Fig. 11.1 Assembly of a hypergroup 

C.T.E. channel translating equipment 
G.T.E. group translating equipment 
S.T.E. supergroup translating equipment 
H.T.E. hypergroup translating equipment 

A coaxial system is built up by assembling the appropriate 
number of 12-channel C.C.I.T.T. groups [TSII]. Fig. 11.1 
shows how the 900 and 10 800 channel coaxial systems are 
assembled. Five 12-channel groups are combined by the group 
translating equipment to form a 60-channel supergroup oc- 
cupying the frequency band 312-552 kHz. In the next stage of 
assembly 15 supergroups are combined to form a 900-channel 
system known as a supermastergroup. The 900-channel system 
is sometimes transmitted to line in its own right. To obtain a 
larger capacity 12 MHz or 60 MHz coaxial system, a number 
of supermastergroups are used to modulate different carrier 
frequencies in order to assemble them alongside one another 
in the appropriate frequency band. In the example shown in 
the figure, 12 supermastergroups are combined by a hyper- 
group translating equipment to form a 10 800-channel hyper- 


group. The carrier frequencies used at each stage in the 
assembly of the system are given in the preceding volume 

Single-sideband amplitude modulation is used at each stage 
of frequency translation at both the transmitting and receiving 
ends of the system. The building block approach to the assem- 
bly of a system is used since it reduces the number of mod- 
ulators and different filters which are needed. At each stage of 
frequency translation at the receiving end of the system, a 
locally-generated carrier must be fed into the balanced mod- 
ulator. The C.C.IT.T. recommendation is for the re-inserted 
carrier to be accurate to within ±2Hz of the carrier frequency 
suppressed at the other end of the system. The highest carrier 
frequency used in the 60 MHz system is 68 200 kHz and so the 
necessary frequency stability is ±3 parts in 10 8 . To achieve 
such a high stability it is necessary to synchronize the carrier 
frequency generating equipment in a repeater station to a pilot 
carrier which is transmitted with the multiplex signal. Modern 
carrier generating equipments are extremely accurate and sta- 
ble, and the generating frequencies need only be compared 
with the pilot carrier at regular intervals of time. The 60 MHz 
multiplex signal is amplified and equalized at 1.5 km intervals 
along the length of the line. At the receive end of the system, 
the signal receives further amplification and equalization be- 
fore it is applied to the translating equipment to be broken 
down into its individual channels. 

Radio Relay Systems 

Radio relay systems using line-of-eight transmissions in the 
u.h.f. and s.h.f. bands can provide a large number of telephone 
channels and/or a television signal. Table 11.2 lists the systems 
that are currently operated in the United Kingdom. 

Table 11.2 

Frequency band Number of Number of 

MHz r.f. channels telephone channels Television 

























Radio relay systems are operated in the upper part of the 
u.h.f. band and in the s.h.f. band because it is then possible to 
provide a bandwidth of several megahertz. A wideband system 
is needed to accommodate several hundreds of telephone chan- 


nels or a television channel. At these frequencies high gain 
aerials of reasonable physical size are available which make it 
possible to use transmitted powers of only a few watts. 
Further, the high directivity obtained minimizes interference 
from and to other systems. 

The BASEBAND SIGNAL (the multiplex signal produced 
by a coaxial multi-channel system or a television camera) is 
used to frequency-modulate a 70 MHz carrier wave. The mod- 
ulated signal is then translated to the allocated frequency 
band. Frequency modulation is used in preference to amp- 
litude modulation for two main reasons. Firstly, an f.d.m. 
telephony baseband signal requires a very linear transfer 
characteristic (output/input) for all the sections of a relay 
system if inter-channel crosstalk, arising from intermodulation, 
is to be avoided. The necessary linearity is much easier to 
provide if frequency modulation is used. Secondly, the use of 
frequency modulation provides an increase in the output 
signal-to-noise ratio of the system. The C.C.I.R. recommend 
the frequency deviations to be used; these are 140 kHz per 
channel for both 960 and 1800 channels systems. 















Separating Separating 
filter filter 



T3 a- 

4- <u 












Fig. 11.2 Radio relay system (Rx receiver, Tx transmitter) 

The basic block diagram of a RADIO RELAY SYSTEM is 
given in Fig. 11.2. Only one relay station has been shown but 
usually several will be used, the actual number depending 
upon the length of the route. 

At the transmit terminal, the baseband signal is pre- 
emphasized and is then used to frequency-modulate a 70 MHz 
carrier. The modulated wave is then shifted to the allocated 
part of the frequency spectrum and amplified before it is 
radiated by the parabolic dish aerial. At the relay station, the 
received signal has its frequency changed back to 70 MHz 
before it is amplified and then shifted back to the frequency 
band to be used over the next section of the route. At the 
receiving end of the system, the signal is reduced in frequency 

telephony baseband 


to 70 MHz before it is demodulated and, finally, the baseband 
signal is passed through the de-emphasis circuit to be restored 
to its original amplitude relationships. 

Fig. 11.3 shows in more detail the equipment used at the 
TRANSMITTING end of the system. The input baseband 
signal can be a 960 or a 1800 channel f.d.m. telephony system 
or a television signal. The telephony signal occupies a band- 
width of 60 kHz-4028 kHz or 316-8248 kHz, i.e. 3.97 MHz or 
7.93 MHz, while the television signal bandwidth is 8 MHz. 







(70 MHz) 







< > baseband input 

Fig. 11.3 Transmitter in a radio relay system 

The baseband signal is pre-emphasized before it frequency- 
modulates a 70 MHz carrier wave. Different de-emphasis net- 
works are used for telephony and for television signals 
(characteristics shown in Fig. 2.10) but otherwise the same 
items of equipment are used. The frequency-modulated signal 
is amplitude limited to remove any amplitude modulation 
present and is then amplified before it is translated to the 
required frequency band by the mixer stage and its following 
low-pass filter. This filter selects one sideband of the mixing 
process. The translated signal is then further amplified to the 
required transmitted power level, typically 10 W, and is then 
passed on to the aerial via an isolator and another filter. The 
isolator is a ferrite device which will only allow signals to pass 
in one direction and it is used to prevent any unwanted signals 
picked up by the aerial passing into the transmitting equip- 
ment. Any reflected signals caused by mismatch at the aerial 
terminals will also be stopped from reaching the equipment. 
The final band-pass filter is provided to band-limit the trans- 
mitted signal in order to avoid interference with adjacent 







70 MHz 








baseband output 





baseband output 

Fig. 11.4 Receiver in a radio relay system 

The block schematic diagram of a RADIO RELAY SYS- 
TEM RECEIVER is given by Fig. 11.4. The received signal is 
selected by the band-pass filter, which rejects any unwanted 
signals that are also picked up by the aerial, and then is 
translated to the 70 MHz intermediate frequency of the re- 
ceiver. The intermediate-frequency signal is amplified, group- 
delay equalized, and amplitude limited before it is demod- 
ulated to obtain the baseband signal. The baseband signal is 
passed through the appropriate de-emphasis network in order 
to restore its frequency components to their original amplitude 
relationships with one another. 

The equipment used in a relay station consists of the back-to- 
back connection, at the intermediate frequency, of a receiver 
and a transmitter equipment. The output of the limiter in the 
receiver diagram is at 70 MHz and this is directly connected to 
the input of the i.f . amplifier shown in the transmitter diagram. 

The parabolic reflector aerials used with radio relay 
systems have the capability to transmit or receive more than 
one r.f. channel at the same time. It is therefore usual for more 
than one r.f. channel to be multiplexed onto a single aerial. To 
improve the discrimination between channels, adjacent (in 
frequency) channels use alternate planes of polarization. For 
example, if channel 1 is horizontally polarized, channel 2 will 
be vertically polarized, channel 3 will be horizontally 
polarized, and so on. The block diagram of the equipment 
involved is shown in Fig. 11.5. As before only one relay 
station is shown but usually there will be several more. A 
circulator is a ferrite device with four input/output terminals; 
the operation of the device is such that a signal entering one 
pair of terminals will be directed only to one other pair of 
terminals — none of the input energy will appear at the other 
two pairs of terminals. 

Both radio relay and coaxial systems are widely used as 
integral parts of the national telephone network. The two 
systems have a number of advantages and disadvantages rela- 
tive to one another which often means that one or the other is 
best suited for providing communication over a given route. 






Ch. 1 

Fig. 11.5 Method of transmitting several r.f. channels over a 
single radio relay system 

The relative merits of the two systems are listed below: 

(a) A radio relay system is generally quicker and easier to 

(b) The problems posed by difficult terrain are easier to 
overcome using a radio relay system. 

(c) It is easier to extend the channel capacity of a radio 
relay system. 

{d) Difficulties may be experienced in obtaining suitable 
(line-of -sight distance) sites for a radio relay system. 

(e) When relay station sites have been chosen it may be 
difficult to gain access to them, whereas coaxial systems 
usually follow roads and so access is relatively easy. 

(/) The transmission performance of a radio relay system is 
adversely affected by bad weather conditions. 

Submarine Cable Systems 

Submarine coaxial cable [TSII] is designed for the transmission 
of wideband signals beneath the seas and oceans. It can 
provide large numbers of good quality, highly reliable, tele- 
phone channels over long distances, for example between 
Europe and North America. 

A single coaxial pair is used for both directions of transmis- 
sion, transmission in one direction being achieved in one 
frequency band with transmission in the opposite direction in a 


n supergroups 

n +m supergroups 

n + m supergroups 
positioned in high-frequency 
transmission band 

m supergroups 
o •— — 


m supergroups 
£,., raised in 


n supergroups 


m supergroups 
O— — « 


__To submarine 

n+m supergroups 
-positioned in low-frequency 
transmission band 

m supergroups 
raised in frequency 

Fig. 11.6 Terminal equipment of a submarine cable system 

higher band. For example, the CANTAT II system between 
the United Kingdom and Canada uses the frequency band 
312-6012 kHz in one direction and the frequency band 8000- 
13 700 kHz in the other. Further, 3 kHz bandwidth telephone 
channels are provided, instead of the 4 kHz channels custom- 
ary in land systems, to economize in the use of the frequency 
spectrum. This means that the bandwidth occupied by a nor- 
mal supergroup, i.e. 60 X 4 kHz = 240 kHz, can now accommo- 
date 80 telephone channels. Fig. 11.6 shows, in block diagram- 
matic form, the equipment used at a terminal which is trans- 
mitting signals in the higher frequency band and receiving 
signals in the lower frequency band. A number n of super- 
groups are assembled in the usual manner (see Fig. 11.1), and 
are combined in a hybrid coil with a number m of other 
supergroups that have been translated to a higher part of the 
frequency spectrum by a stage of modulation. The combined 
(m + n) supergroups are next positioned in the high-frequency 
transmission band by another stage of modulation and then 
applied to the input terminals of the submarine cable. Incom- 
ing supergroups are positioned in the lower frequency band 
and do not require demodulation before being separated into 
two groups of n and m supergroups. 

High-frequency Radio Systems 

Submarine cable systems are extremely expensive and their 
traffic capacity is not sufficient to satisfy the ever-increasing 
demand for international communication facilities. Some long- 

Fig. 11.7 Communication satellite system 




distance international circuits are provided in the 3-30 MHz 
high-frequency band. Modern high-frequency systems can pro- 
vide a fairly reliable service and for most of the time although 
sometimes propagation conditions are such that communica- 
tion by this means is not possible. High-frequency radio sys- 
tems have the advantages of (a) a relatively low capital cost 
and (b) flexibility; and it is expected that they will find con- 
tinued application as a supplement to submarine cable and 
communication satellite systems. 

Communication Satellite Systems 

Most of the long-distance international telephone traffic which 
is not carried by submarine cable systems is routed via a 
broadband communication satellite system, the basic principle 
of which is illustrated by Fig. 11.7. The ground stations are 
fully integrated with their national telephone networks and, in 
addition, the European ground stations are fully intercon- 
nected with one another. Four frequencies are used; the North 
American ground station transmits on frequency ft and receives 
a frequency / 4 , the European stations transmit frequency f 3 
and receive frequency / 2 . Essentially, the purpose of the 
communication satellite is to receive the signals transmitted to 
it, frequency translate them to a different frequency band (/ x 
to f 2 or f 3 to / 4 ), amplify the signals, and then re-transmit them 
to the ground station at the other end of the link. 

Communication satellites which form an integral part of the 
public international telephone network are operated on a 
global basis by COMSAT (Communication Satellite Corpora- 
tion) on behalf of an international body known as INTELSAT 


(International Telecommunication Satellite Consortium). The 
COMSAT system employs communication satellites travelling 
in the circular equatorial orbit at a height of 35 880 km. This 
particular orbit is known as the synchronous orbit because a 
satellite travelling in it appears to be stationary above a 
particular part of the Earth's surface. Seven satellites are used, 
positioned around the Earth so that nearly all parts of the 
surface of the Earth are "visible" from at least one satellite. A 
large number of ground stations are in use and now number 
more than a hundred in nearly a hundred different countries. 

Each ground station transmits its telephone traffic to a 
satellite on the particular carrier frequency allocated to it in 
the frequency band 5.925-6.425 GHz. This is a bandwidth of 
500 MHz and allows the simultaneous use of a satellite by 
more than one ground station. Different ground stations are 
allocated different carrier frequencies within this 500 MHz 
band, either permanently or for particular periods of time — 
depending on the traffic originated by that station. This 
method of utilizing the capacity of a communication satellite is 
known as frequency division multiple access (f.d.m.a.). Each of 
the allocated carrier frequencies has a sufficiently wide band- 
width to allow a multi-channel telephony system to be trans- 
mitted and, in some cases, a television channel. The number of 
telephony channels thus provided varies from 24 in a 2.5 MHz 
bandwidth to 1872 in a bandwidth of 36 MHz. All the signals 
transmitted by a satellite are transmitted towards every ground 
station and each station selects the particular carrier frequen- 
cies allocated to it in the band 3.700-4.200 GHz. 

Noise and Interference in Communication Systems 

The output of any communication system, line or radio, will 
always contain some unwanted components superimposed 
upon the desired signal waveform. The unwanted voltages are 
the result of noise and interference picked up by or generated 
within the system. The sources of noise and interference in 
communication systems are many and have been discussed 
elsewhere [EIII]. This section will deal with noise and interfer- 
ence in multi-channel radio-relay systems. 

Thermal noise voltages developed in the input stages of a 
receiver, either in a relay station or at the terminal station, will 
have an effect on the output signal-to-noise ratio which varies 
with the level of the incoming signal. When the incoming 
signal level is low, the a.g.c. action of the receiver will increase 
the gain of the receiver in an attempt to maintain the output 
voltage at a more or less constant level; unfortunately this 
means that the thermal noise generated in the input stage will 
be amplified to a greater extent. The other main source of 




r== ^^ r ^^ r 4^^ r 4^ r =4=^ 


Interferencing signal 



rC^--"' >*X 


Fig. 11.8 Co-channel interference in a radio relay system 

noise appearing at the output of the system is known as 
intermodulation noise. Intermodulation noise is produced by 
non-linearity in the amplitude/frequency and the group-delay 
frequency characteristics of the various parts of the system. 
Intermodulation noise has components at most frequencies 
and so sounds very much like thermal agitation noise. How- 
ever, whereas thermal noise is continually produced inter- 
modulation noise increases with increase in the signal level. 

Adjacent-channel interference can occur on routes where all 
the available carrier frequencies are in use and therefore 
adjacent in-frequency carriers must be employed. Clearly, this 
form of interference can be minimized by the use of receivers 
of adequate selectivity. Co-channel interference can also exist 
if signals proper to one receive aerial are able to overshoot 
and be picked up by another aerial further along the route (see 
Fig. 11.8a). To reduce co-channel interference arising from 
this effect, two frequencies f t and f 2 can be allocated for use as 
carriers and alternate relay stations can use the same fre- 
quency (Fig. 11.8b). To reduce still further this form of 
interference, the path followed by the route can be zig-zagged 
in the manner shown in Fig. 11.8c; however the possibility of 
co-channel interference is not eliminated, as shown. 


Choice of Carrier Frequency and Bandwidth 

To enable the best use to be made of the available frequency 
spectrum, amplitude or frequency modulation of a carrier 
wave of appropriate frequency is used. Multi-channel tele- 
phony systems employ frequency-division multiplex and for 
each channel in the system the carrier frequency, or frequen- 
cies if more than one stage of modulation is used, must be 
chosen to position that channel in a particular part of the 
system bandwidth. To obtain the maximum utilization of the 
transmission medium (coaxial cable or radio relay system), the 
audio, group and r.f. bandwidths must be as narrow as possible 
whilst passing all the significant components of the signal 
waveform. For a line coaxial system the lowest frequency 
transmitted to line is determined by the need to avoid opera- 
tion at the lowest frequencies where the attenuation/frequency 
characteristic of the cable is markedly non-linear. At the other 
end of the frequency spectrum, the higher the maximum 
frequency that is transmitted to line the greater is the attenua- 
tion of the line at that frequency and the closer must be the 
spacing between the line repeaters. Thus the maximum fre- 
quency to be transmitted is very largely determined by the 
minimum repeater spacing which can be economically jus- 

To minimize the number of modulators and demodulators 
and the associated circuitry needed, a coaxial telephony system 
is assembled by suitably combining a number of C.C.I.T.T. 
12-channel groups. The filters used to separate the audio 
channels are required to attenuate signals which are more than 
600 Hz outside the 3.1kHz channel bandwidth by at least 
70 dB. To achieve such a high order of selectivity crystal filters 
[TSII] must be used. When the carrier frequencies for the 
12-channel groups were originally chosen, crystal filters were 
only economically available at frequencies in excess of about 
60 kHz. For this reason the channel carrier frequencies start at 
64 kHz for channel 12 and increase in 4 kHz steps for each 
channel up to 108 kHz for channel 1. The lower sidebands for 
each channel are selected and so the bandwidth occupied by a 
group is 60.6-107.7 kHz, i.e. approximately 60-108 kHz. 

Larger capacity systems are built up by suitably combining 
12-channel groups. The ways in which the 12-channel groups 
can be combined have been specified by the C.C.I.T.T. and 
one example has been given earlier in this chapter (Fig. 11.1). 

Multi-channel telegraphy systems are capable of transmit- 
ting 24 channels over a commercial quality speech circuit. The 
choice of carrier frequencies for the individual channels is 
primarily determined by the need to minimize inter-channel 
interference. Any non-linearity in the system will generate 

Low group 


harmonic and intermodulation products, the most important of 
which, since they are of the greatest magnitude, are 2/ l5 2/ 2 , 
and fi±f 2 where f x and f z are two carrier frequencies. To 
minimize interchannel interference, the channel carrier fre- 
quencies are chosen to be the odd harmonics of 60 Hz, starting 
with the seventh. This means that the channel 1 carrier fre- 
quency is 420 Hz, channel 2 carrier frequency is 540 Hz, and 
so on up to channel 24 whose carrier frequency is 3180 Hz. 
The channel bandwidth is 50 Hz [TSII]. 

Wideband radio-relay systems must operate in the u.h.f . and 
s.h.f. bands because of the very wide bandwidths they occupy. 
Various frequency bands, listed in Table 11.2, have been 
allocated for this purpose by the I.T.U. (International Tele- 
communication Union). The C.C.I.R. issue recommendations 
regarding the division of each frequency band into a number 
of r.f. channels and, for example, Fig. 11.9 gives the recom- 
the 5925-6425 MHz band. The 500 MHz 
vided into a low and a high group of frequen- 

High group 

bandwidth is 






lh lh 








6404.79 MHz 




6375.14 MHz 

Fig. 11.9 Frequency allocation of a radio relay system 

cies. At any particular relay station, all the transmitting chan- 
nels are given carrier frequencies in one group and all the 
receiving channels have carrier frequencies in the other group. 
For example, at one station r.f. channels may be transmitted 
on low-group frequencies and received on carrier frequencies 
in the high group. Also, as shown in Fig. 11.8b, an r.f. channel 
received on a low-group carrier frequency at a relay station 
will be transmitted on the corresponding high-group carrier 
frequency, e.g. a channel received at a carrier frequency of 
6004.5 MHz would be re-transmitted at 6256.54 MHz. 



11.1. Give an outline description of a typical microwave radio-relay 
system for carrying television and multi-channel telephony 
signals. Discuss the factors that would influence the choice of 
radio frequencies to be used for the system. 

11.2. Discuss the sources of noise and interference in a multi- 
channel radio-relay system. 

11.3. (a) Why is frequency modulation used in radio relay links in 
preference to amplitude modulation? (b) Why is pre-emphasis 
used for (i) multi-channel telephony and (ii) television signals? 
(c) Draw the pre-emphasis characteristic used in each case. 

11.4. Draw the block diagrams of (a) the transmitter and (b) the 
receiver of an s.h.f. radio-relay link. 

11.5. Describe, with the aid of diagrams, a multi-channel telephony 
system for use with a submarine coaxial cable. 

11.6. Describe, with the aid of diagrams, a multi-channel telephony 
system for use in the inland telephone network. 

11.7. Explain, with the aid of diagrams, what is meant by the terms 
supergroup and hypergroup. How may a multi-channel tele- 
phony system be transmitted over a s.h.f. radio-relay system? 

11.8. Draw, and explain, the block schematic diagram of the repea- 
ter in a s.h.f. radio-relay system. 

Short Exercises 

11.9. Where and why in a radio relay system might (a) an isolator, 
(b) a circulator be used? 

11.10. List the causes of interference in multi-channel radio-relay 

11.11. State the reasons why pre-emphasis is applied to the television 
and multi-channel telephone baseband signals in a radio relay 

11.12. What is meant by the term frequency-division multiplex and 
why is it used? 

N u merica I Answers to 

1.2 41.67 W 1.6 360 V, 180 V 
1.8 0.6325, 1.2 mW 1.9 0.33 

1.11 (i) 990 kHz, 1000 kHz, 1010 kHz, (ii) 990 kHz, 

1010 kHz, (iii) 990 kHz or 1010 kHz 
1.13 8000 Hz 1.14 8000 Hz 1.15 0.4 1.17 3.147 V 
2.1 70 kHz 2.3 8, 180 kHz 2.5 8.18% 

2.7 46 kHz 2.8 66 kHz, 36 kHz, 6 dB down 
2.15 Many possible answers 2.19 20 kHz 
3.23 2045 Hz 

4.3 1.2 4.4 L = 312 nH, C = 55.55 pF 

4.5 0.024 4.8 (c) 5.657 dB assuming G = 
4.11 5 V 4.12 0.375 

5.13 26 dB 5.14 25%, 100 W 

5.18 125 MHz, 5.23 1.291 m, 1.291 km 

6.11 2.4 MW 

7.1 408.33 W, 408.33 W 7.2 750 W, 300 W, 77.5% 

7.8 3496 W, 14 124 W 7.11 0.833 A 

7.14 1.57 A, 36070 A 7.15 214.3 W 

8.9 7.07 MHz 8.11 D = 27, D = 1.5 8.12 6.842 
9.1 40 pF, 195.5 j^H, 283.3 pF, 140.7 ju,H 

9.3 0,0,4 kHz 9.4 92.6 pF 9.5 3.33 kHz 

9.13 40 pF, 232.6 /u,H, 258.3 pF 

9.14 150.7 MHz, 129.3 MHz 


Radio Systems III: 
Learning Objectives (TEC) 


(A) Radio Systems 

page 207 (1) Surveys radio communication systems in the public service. 
209 1.1 Describes the use of high-capacity s.h.f. relay systems for 

tv and telephony. 
208 1.2 Describes a high-capacity coaxial system. 
210, 211, 212 1.3 Describes interface equipment between a line system and 

a radio system. 
216 1.4 Outlines origins of noise and distortion in transmission 

218 1.5 Describes factors affecting choice of frequencies and 

bandwidths for line and radio transmission including: 

(a) multi-channel telephony and telegraphy 

(b) tv systems. 

100-16 1.6 Describes factors affecting radio propagation up to 

300 MHz. 
100-16 1.7 Describes effects of ground, ionosphere and troposphere 

in 1.5. 
115 1.8 Lists applications of propagation below 300 MHz. 

(B) Principles of Modulation 

1 (2) Understands principles and practice of different forms of 
amplitude modulation 
4, 13 2.1 Describes the components of d.s.b. s.s.b. (pilot carrier 
and suppressed carrier) and i.s.b. by reference to graphi- 
cal diagrams. 
2.2 Explains how an s.s.b.s.c. signal is produced. 

45 (a) by the filter method 

46 (b) by the phasing method 

52 2.3 Explains in detail with the aid of diagrams, the demod- 
ulation of a d.s.b. signal. 
52, 53, 54 2.4 Draws circuit diagrams relating to 2.3. 


page 52 2.5 Describes detector distortions which may occur in the 
demodulation of d.s.b. 
41, 54 2.6 States the requirements for demodulation of a s.s.b.s.c. 
signal in terms of heterodyne oscillation magnitude (rela- 
tive to signal magnitude) and frequency. 

56 2.7 Describes a heterodyne detector for s.s.b.s.c. demodula- 

55 2.8 Demonstrates the effects of distortion relating to 2.5 and 

15 2.9 Measures salient factors of d.s.b. and s.s.b. signals. 

20 (3) Understands the principles and practice of frequency mod- 
28 3.1 Explains the relationships between frequency and phase 
21, 23 3.2 Defines deviation, modulation index and deviation ratio. 
24 3.3 Describes graphically the magnitude of carrier and low 

order sidebands in an f .m. signal. 
36 3.4 Measures deviation by carrier disappearance method. 
26, 30 3.5 States typical deviations used in high quality transmission 
and in narrow band f.m. systems. 
47 3.6 Describes the operation of a reactance modulator circuit. 
30 3.7 Describes pre- and de-emphasis in f.m. speech proces- 
150, 151 3.8 Draws an f.m. transmitter in block diagram form. 
157, 159 3.9 Describes the f.m. receiver with the aid of block dia- 
3.10 Explains the operation of: 

28, 58,60 (a) the limiter 

56 (b) the discriminator 

203 (c) the squelch circuit 

177 (d) a.f.c. 

35 3.11 Explains the capture effect. 

(C) The Superheterodyne Receiver 

157 (4) Reviews and extends knowledge of the superheterodyne 

167 4.1 States factors affecting sensitivity. 
183 4.2 Measures the performance of an a.m. superheterodyne in 

terms of sensitivity, noise factor, adjacent and image 

channel ratios. 
169 4.3 Calculates oscillator tracking errors for simple cases. 
169 4.4 States required performance of a local oscillator in terms 

of drift and stability. 
148, 180, 183 4.5 Describes the synthesised local oscillator for precision 

175 4.6 States need for automatic gain control. 

224 RADIO SYSTEMS III: learning objectives (tec) 

page 198, 199 4.7 Describes simple and delayed a.g.c. circuits and their 
165, 186 4.8 Sketches selectivity curves required in the presence of 
195 4.9 Describes a simple i.f. crystal filter. 

(D) Radio Transmitters 

118 (5) Understands the principles and practice of r.f. power stages. 
118 5.1 States the need for high efficiency in transmitter final 

140 5.2 States the function of a tuned power amplifier. 
120, 127 5.3 Draws diagrams of anode/collector current and voltage 

pulses in relation to drive in Class B and Class C stages. 

121 5.4 States the need for signal drive into the "positive" 

127 5.5 Calculates that the theoretical maximum efficiency of a 
Class B stage is 78.5%. 

122 5.6 States typical angle of flow in Class C stages. 

118, 128 5.7 States typical attainable efficiencies in Class B and Class 
C stages. 
122 5.8 Explains the effects of varying factors such as angle of 

flow and loading. 
119 5.9 Explains why high level modulation is common practice 
for a.m. transmitters. 
131, 132, 134 5.10 Draws simplified circuits of high-level-modulated Class B 
and C stages. 
133 5.11 Calculates modulator power requirements. 
144 5.12 Explains methods of tuning and loading a power stage to 

a line or transmitting aerial. 
136 5.13 Describes special features of v.h.f. techniques in r.f. 

power stages. 
146 5.14 Describes special features of mobile and miniature re- 
136, 152 5.15 Describes the special features of h.f. and high power 
components, devices and valves. 
153 5.16 States special hazards relating to high voltage high fre- 
quency equipment. 

(E) Aerials 

81 (6) Understands the principles and use of aerials in transmission 
and reception. 

86 6.1 Describes how the A/2 dipole may be developed into the 

folded dipole. 

87 6.2 States a typical driving point impedance of a folded 


88 6.3 Describes the Rhombic aerial and its characteristics. 
91 6.4 Describes the Log-Periodic aerial and its properties. 


Aerials 81 

Dipole, A/2 82 

folded dipole 86 

gain of 85, 90, 94, 96 

input impedance of 83, 90, 94 

log-periodic 91 

parabolic reflector 95 

radiation pattern of 83, 84, 89, 93, 94, 97 

rhombic 88 

two-dipole array 92 

use of director 85 

use of reflector 84 

Amplitude modulation 1 

bandwidth 3 

depth of modulation 5 

d.s.b.s.c. 9 

indepdendant sideband 12 

measurement of 15 

merits of, relative to f.m. 35 

modulation envelope 2 

modulation factor 5 

peak-envelope power 12 

power content 6 

principles of 1 

r.m.s. value of 8 

sideband 3 

sidefrequency 2 

s.s.b.s.c. 10 

s.s.b.s.c. merits relative to d.s.b. 11 

vestigial sideband 14 
Angle modulation 27 
Anode modulated r.f. amplifier 131 
Attenuation coefficient, of a line 68 
Audio-frequency stage, in radio receiver 179 
Automatic frequency control 177, 202 
Automatic gain control 175, 198 

application to controlled stage 200 

delayed 199 

f.m. receiver 199 

simple 198 

Balanced demodulator 54 
Balanced modulator 10, 40 

of a.m. wave 3 
of f.m. wave 26 

Ceramic filter 197 

Characteristic impedance, of a line 68 

Choice of carrier frequencies and bandwidths 214 

Coaxial telephony systems 

land 208 

submarine 213 
Collector modulated r.f. amplifier 134 
Communication receiver 

i.s.b. 180 

v.h.f. 182 
Communication satellite systems 215 

De-emphasis in f.m. systems 32 
Demodulators 51, 56, 175 
amplitude 51 

balanced 54 

diode detector 52 

heterodyne 56 

product 55 

transistor detector 54 
frequency 56 

Foster-Seeley 56 

phase-locked loop 62 

quadrature detector 61 

ratio detector 59 
Depth of modulation 5 
Detectors, see Demodulators 
Deviation ratio 23 
d.s.b. amplitude modulation 1 
d.s.b.s.c. amplitude modulation 9 

Fading, of radio waves 113 
Feeders, in radio systems 78 

ceramic 197 

crystal 195 
Foster-Seeley discriminator 56 
Frequency modulation 20 

bandwidth 26 

de-emphasis 32 

deviation ratio 23 


226 INDEX 

frequency deviation 21 

frequency spectrum 24 

frequency swing 23 

measurement of 36 

merits of, relative to a.m. 35 
relative to phase modulation 35 

modulation index 23 

phase deviation 23 

power content 27 

pre-emphasis 31 

principles of 20 

rated system deviation 22 

signal-to-noise ratio 28 

triangular noise spectrum 28 
Frequency multiplication 130 
Frequency synthesis 148, 179 
Frequency wavebands 101 

use of 115 

Ganging 169 
Ground wave 104 

Heterodyne detector 56 

High frequency radio systems 214 

High voltage precautions in radio transmitters 152 

Ionosphere 101 
Independant sideband 12 
Intermediate frequency 158 
Intermediate frequency amplifier 174 

Land coaxial cable systems 208 
Log-periodic aerials 91 

high-frequency 94 

v.h.f. dipole 92 

of amplitude-modulated waves 15 
of frequency-modulated waves 36 
of radio receivers 183 
adjacent channel selectivity 185 
image channel response ratio 186 
noise figure 184 
sensitivity 184 
Measurement, of v.s.w.r. 39 
Mixer 168, 190 
Modulators, amplitude 39 
d.s.b. 39 
s.s.b. 40 
single balanced 42 
double balanced 44 
integrated 44 
Modulation factor 5 
Modulation index 23 
Muting, in radio receivers 203 

Noise, and interference in communication systems 216 
Noise figure 167 
measurement of 184 

Output stage, of radio transmitter 145 

Parabolic reflector aerial 95 

Peak envelope power 12 

Phase change coefficient, of a line 70 

Phase modulation 27 

Phase-locked looped detector 62 

Phase velocity, of a line 70 
Pre-emphasis, of f.m. wave 30 
Product detector 55 
Propagation of radio waves 100 
fading 113 

selective 114 
ground wave 104 
ionosphere 101 

refraction of an electromagnetic wave 105 
sky wave 106 

critical frequency 108 
l.u.f. 110 
m.u.f. 109 
multi-hop links 111 
skip distance 111 
space wave, direct 111 

via satellite 112 
tropospheric scatter 112 

Quadrature amplitude modulation 14 
Quadrature detector 61 

Radio-frequency power amplifiers 118 
anode modulated Class C 131 
Class B transistor 129 

valve 125 
Class C transistor 129 
valve 119 
angle of flow 122 
anode efficiency 123 
earthed grid operation 124 
power relationships 123 
collector modulated Class C 134 
Frequency multiplier 130 
v.h.f. techniques 136 
Radio-frequency stage, in a radio receiver 168 
Radio relay systems 209 
receiver 212 
transmitter 211 
Radio station feeders 78 
Ratio detector 59 
Reflection coefficient, of a line 74 
Rhombic aerial 88 

Selective fading, of radio waves 114 
Sideband suppression, 
filter method 45 
phase shift method 46 
Squelch, in a radio receiver 203 
Standing wave, on a line 73 
Standing wave ratio 76 
Superheterodyne radio receiver 157 

audio-frequency amplifier 179 

automatic frequency control 177 

automatic gain control 175, 198, 199 

blocking 165 

co-channel interference 163 

crossmodulation 164 

double superhet 179 

detector stage 175 

ganging and tracking 169 

half i.f. interference 164 

image channel 161 
image response ratio 162 
measurement of 186 

INDEX 227 

intermediate frequency 158 

choice of 174 
i.f. amplifier stage 174 
intermodulation 164 
local oscillator, 

choice of frequency 160 

radiation of 164 
mixer stage 168 
noise figure 167 
r.f. stage 168 
selectivity 165 

measurement of 185 
sensitivity 162, 166 

measurement of 184 

Tracking 169 
Transistor detector 54 
Transmission lines 67 
matched 67 

attenuation coefficient 68 

characteristic impedance 68 

loss-free 69 

phase change coefficient 70 

phase velocity 70 

mismatched 71 
measurement of v.s.w.r. 77 
reflection coefficient 74 
standing wave 73 
standing wave ratio 76 
Transmitters, radio 140 
amplitude modulation 140 
high-level 140 
low-level 141 
i.s.b. 142 
s.s.b. 143 
output stages 145 
self-tuning 144 
v.h.f. mobile 146 
frequency modulation 150 
high-voltage precautions 152 

Velocity of propagation, on a line 70 
V.H.F. techniques, in tuned amplifiers 136 
Voltage standing wave ratio 76 

Wavebands, radio 101 
use of 115 

Yagi aerial 82 

This book describes the operation of modern radio systems and provides an 
eminently suitable text for any non-advanced radiocommumcation course. 

The contents of the book are based on the Radio Systems li! unit of the U K 
Technician Education Council and provide complete coverage of the unit 
The level of treatment assumes the reader to have a knowledge of communi- 
cation systems of the standard reached by the TEC level II units Radio 
Systems II and Transmission Systems II. Also the reader is assumed to have 
studied, or be concurrently studying, electronics theory to the standard of the 
level III unit Electronics III, 

The scope of the book is such that it covers all aspects of radio engineering. 
from amplitude and frequency modulation, r f. transmission lines, aerials and 
radio wave propagation, to the circuits and techniques used in modern radio 
receivers and transmitters. 

vlany worked examples demonstrate the principles and applications involved 
jnd every chapter concludes with test exercises. 

The complete series will include the following titles: 

Telecommunication Systems I Electronics II 

Transmission Systems II Radio Systems III 

Radio Systems II Telephone Switchino Svstems III 

Telephone Switching Systems II Electronics III 

Further specialised titles will be added as the demand arises. The Scientific and 
Technical Editor (SFE Dept) is willing to receive any suggestions for titles by any 
means of communication. 


BN 273 01134